MATLAB Central Newsreader - LMI term dimensions incompatible

LMI term dimensions incompatible

Michael Zhang — Thu, 08 May 2008 04:19:05 -0400

Is anyone can help me? I can figure out what happened to my
programm.

I need to solve a inequality:

| -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
| Q*A'+M'*B2' -Q 0
| B1' 0 -gammar^2*I
| Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
| 0 M 0
| 0 Q 0

    Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
         Q*C'+M'*D12' M' Q |
             D11' 0 0 | <0
  -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
             0 -S2 0 |
             0 0 -S1 |

Matrices:Q, S1, S2 are positive-define.

Below is programm:
===================================================
A = [2 1; 0 1];
Ad = [0.2 0.1; 0 0.1];
B1 = [0.1 0.1]';
B2 = [1 1]';
Bd = [0.1 0.1]';

C = [1, 1];
Cd = [0.1, 0.1];

D11 = 0.1;
D12 = 1;
Dd = 0.1;

gammar = 1;

% Initial a LMI system
setlmis([]);

% Define Variables

% Q is a symmetric matrix, has a block size of 2 and this
block is symmetric
Q = lmivar(1, [2 1]);

% S1 a symmeric matrix, size 2 by 2
S1 = lmivar(1, [2 1]);

% S2 is 1 by 1 matrix
S2 = lmivar(1, [1 0]);

% Type of 2, size 1 by 2
M = lmivar(2, [1 2]);

%I use upper triangular to represent the LMI

% pos in (1, 1)
lmiterm([1 1 1 Q], -1, 1);
lmiterm([1 1 1 S2], Bd, Bd');
lmiterm([1 1 1 S1], Ad, Ad');

% pos (1, 2)
lmiterm([1 1 2 Q], A, 1);
lmiterm([1 1 2 M], B2, 1);

% pos(1, 3)
lmiterm([1 1 3 0], B1);

% pos(1, 4)
lmiterm([1 1 4 S2], Bd, Bd');
lmiterm([1 1 4 S1], Ad, Cd');

% pos(2, 2)
lmiterm([1 2 2 Q], -1, 1);

% pos(2, 4)
lmiterm([1 2 4 Q], 1, C');

lmiterm([1 2 4 -M], 1, D12');

% pos(2, 5)
lmiterm([1 2 5 -M], 1, 1);

% pos(2, 6)
lmiterm([1 2 6 Q], 1, 1);

% pos(3, 3)
lmiterm([1 3 3 0], -(gammar^2));

% pos(3, 4)
lmiterm([1 3 4 0], D11');

% pos(4, 4)
lmiterm([1 4 4 0], -1);
lmiterm([1 4 4 S1], Cd, Cd');
lmiterm([1 4 4 S2], Dd, Dd');

% pos(5, 5)
lmiterm([1 5 5 S2], -1, 1);

% pos(6, 6)
lmiterm([1 6 6 S1], -1, 1);

lmis = getlmis;

[tmin, feas] = feasp(lmis)

--------------------------------
When I run it, I get error message:

??? Error using ==> lmiterm at 296
lhs of LMI #1, block (4,1): term dimensions incompatible
with
other terms in same row

Error in ==> paperor at 56
lmiterm([1 1 4 S1], Ad, Cd');

I have checked many times and can't figure out why it is
wrong, can anybody point it to me?

Re: LMI term dimensions incompatible

Johan Löfberg — Thu, 08 May 2008 08:49:04 -0400

Well, I won't directly answer your question, but when I see
this, I can see that it must be annoying. My advice to you
is to use more modern tools to setup and solve the SDP.

Using YALMIP and the solver SeDuMi
http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php
http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?n=Solvers.SEDUMI

you would code your problem as below.

I think this approach would save you a lot of agony during
the modelling.

/johan

Q = sdpvar(n,n);
S1 = sdpvar(n,n);
S2 = sdpvar(n,n);

gammasquared = sdpvar(1,1);

A = randn(n,n);
Ad = randn(n,n);
Bd = randn(n,n);
B1 = randn(n,n);
B2 = randn(n,n);
M = randn(n,n);
Cd = randn(n,n);
C = randn(n,n);
D11 = randn(n,n);
D12 = randn(n,n);
Dd = randn(n,n);

% We could do something like this, but then we would have to
find out the
% dimensions of the zero blocks, and we are too lazy to do that
%B = [ -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
       Bd*S2*Dd'+Ad*S1*Cd' 0 0;
% Q*A'+M'*B2' -Q 0
    Q*C'+M'*D12' M' Q;
% B1' 0 -gammasquared*I
         D11' 0 0;
% Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
  -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0;
% 0 M 0
     0 -S2 0;
% 0 Q 0
     0 0 -S1 ];

% Instead, we use the blkvar shortcut. It automatically
fills in the blanks and symmetrizes for you
B = blkvar;
B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
B(1,2) = A*Q+B2*M;
B(1,3) = B1;
B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
B(2,2) = -Q;
B(2,4) = Q*C'+M'*D12';
B(2,5) = M';
B(2,6) = Q;
B(3,3) = -gammasquared*eye(size(B1,2));
B(3,4) = D11';
B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
B(5,5) = -S2;
B(6,6) = -S1;

% set up all constraints
Constraints = [B < 0, Q>0, S1>0, S2>0];
Objective = gammasquared;
% Minimize gamma^2
solvesdp(Constraints,Objective)

"Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
<fvtuvp$aiv$1@fred.mathworks.com>...
> Is anyone can help me? I can figure out what happened to my
> programm.
>
> I need to solve a inequality:
>
> | -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
> | Q*A'+M'*B2' -Q 0
> | B1' 0 -gammar^2*I
> | Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
> | 0 M 0
> | 0 Q 0
>
> Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
> Q*C'+M'*D12' M' Q |
> D11' 0 0 | <0
> -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
> 0 -S2 0 |
> 0 0 -S1 |
>
> Matrices:Q, S1, S2 are positive-define.
>
> Below is programm:
> ===================================================
> A = [2 1; 0 1];
> Ad = [0.2 0.1; 0 0.1];
> B1 = [0.1 0.1]';
> B2 = [1 1]';
> Bd = [0.1 0.1]';
>
> C = [1, 1];
> Cd = [0.1, 0.1];
>
> D11 = 0.1;
> D12 = 1;
> Dd = 0.1;
>
> gammar = 1;
>
> % Initial a LMI system
> setlmis([]);
>
> % Define Variables
>
> % Q is a symmetric matrix, has a block size of 2 and this
> block is symmetric
> Q = lmivar(1, [2 1]);
>
> % S1 a symmeric matrix, size 2 by 2
> S1 = lmivar(1, [2 1]);
>
>
> % S2 is 1 by 1 matrix
> S2 = lmivar(1, [1 0]);
>
>
> % Type of 2, size 1 by 2
> M = lmivar(2, [1 2]);
>
>
> %I use upper triangular to represent the LMI
>
> % pos in (1, 1)
> lmiterm([1 1 1 Q], -1, 1);
> lmiterm([1 1 1 S2], Bd, Bd');
> lmiterm([1 1 1 S1], Ad, Ad');
>
> % pos (1, 2)
> lmiterm([1 1 2 Q], A, 1);
> lmiterm([1 1 2 M], B2, 1);
>
> % pos(1, 3)
> lmiterm([1 1 3 0], B1);
>
> % pos(1, 4)
> lmiterm([1 1 4 S2], Bd, Bd');
> lmiterm([1 1 4 S1], Ad, Cd');
>
>
> % pos(2, 2)
> lmiterm([1 2 2 Q], -1, 1);
>
> % pos(2, 4)
> lmiterm([1 2 4 Q], 1, C');
>
> lmiterm([1 2 4 -M], 1, D12');
>
> % pos(2, 5)
> lmiterm([1 2 5 -M], 1, 1);
>
> % pos(2, 6)
> lmiterm([1 2 6 Q], 1, 1);
>
> % pos(3, 3)
> lmiterm([1 3 3 0], -(gammar^2));
>
> % pos(3, 4)
> lmiterm([1 3 4 0], D11');
>
> % pos(4, 4)
> lmiterm([1 4 4 0], -1);
> lmiterm([1 4 4 S1], Cd, Cd');
> lmiterm([1 4 4 S2], Dd, Dd');
>
> % pos(5, 5)
> lmiterm([1 5 5 S2], -1, 1);
>
>
> % pos(6, 6)
> lmiterm([1 6 6 S1], -1, 1);
>
> lmis = getlmis;
>
> [tmin, feas] = feasp(lmis)
>
> --------------------------------
> When I run it, I get error message:
>
> ??? Error using ==> lmiterm at 296
> lhs of LMI #1, block (4,1): term dimensions incompatible
> with
> other terms in same row
>
> Error in ==> paperor at 56
> lmiterm([1 1 4 S1], Ad, Cd');
>
> I have checked many times and can't figure out why it is
> wrong, can anybody point it to me?
>

Re: LMI term dimensions incompatible

Michael Zhang — Thu, 08 May 2008 11:15:07 -0400

"Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
message <fvueq0$mf3$1@fred.mathworks.com>...
> Well, I won't directly answer your question, but when I
see
> this, I can see that it must be annoying. My advice to you
> is to use more modern tools to setup and solve the SDP.
>
> Using YALMIP and the solver SeDuMi
> http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php
> http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?
n=Solvers.SEDUMI
>
> you would code your problem as below.
>
> I think this approach would save you a lot of agony during
> the modelling.
>
> /johan
>
>
> Q = sdpvar(n,n);
> S1 = sdpvar(n,n);
> S2 = sdpvar(n,n);
>
> gammasquared = sdpvar(1,1);
>
> A = randn(n,n);
> Ad = randn(n,n);
> Bd = randn(n,n);
> B1 = randn(n,n);
> B2 = randn(n,n);
> M = randn(n,n);
> Cd = randn(n,n);
> C = randn(n,n);
> D11 = randn(n,n);
> D12 = randn(n,n);
> Dd = randn(n,n);
>
>
> % We could do something like this, but then we would have
to
> find out the
> % dimensions of the zero blocks, and we are too lazy to
do that
> %B = [ -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M
B1
> Bd*S2*Dd'+Ad*S1*Cd' 0 0;
> % Q*A'+M'*B2' -Q
0
> Q*C'+M'*D12' M' Q;
> % B1' 0 -
gammasquared*I
> D11' 0 0;
> % Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M
D11
> -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0;
> % 0 M
0
> 0 -S2 0;
> % 0 Q
0
> 0 0 -S1 ];
>
> % Instead, we use the blkvar shortcut. It automatically
> fills in the blanks and symmetrizes for you
> B = blkvar;
> B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> B(1,2) = A*Q+B2*M;
> B(1,3) = B1;
> B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> B(2,2) = -Q;
> B(2,4) = Q*C'+M'*D12';
> B(2,5) = M';
> B(2,6) = Q;
> B(3,3) = -gammasquared*eye(size(B1,2));
> B(3,4) = D11';
> B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> B(5,5) = -S2;
> B(6,6) = -S1;
>
> % set up all constraints
> Constraints = [B < 0, Q>0, S1>0, S2>0];
> Objective = gammasquared;
> % Minimize gamma^2
> solvesdp(Constraints,Objective)
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> <fvtuvp$aiv$1@fred.mathworks.com>...
> > Is anyone can help me? I can figure out what happened
to my
> > programm.
> >
> > I need to solve a inequality:
> >
> > | -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
> > | Q*A'+M'*B2' -Q 0
> > | B1' 0 -gammar^2*I
> > | Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
> > | 0 M 0
> > | 0 Q 0
> >
> > Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
> > Q*C'+M'*D12' M' Q |
> > D11' 0 0 | <0
> > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
> > 0 -S2 0 |
> > 0 0 -S1 |
> >
> > Matrices:Q, S1, S2 are positive-define.
> >
> > Below is programm:
> > ===================================================
> > A = [2 1; 0 1];
> > Ad = [0.2 0.1; 0 0.1];
> > B1 = [0.1 0.1]';
> > B2 = [1 1]';
> > Bd = [0.1 0.1]';
> >
> > C = [1, 1];
> > Cd = [0.1, 0.1];
> >
> > D11 = 0.1;
> > D12 = 1;
> > Dd = 0.1;
> >
> > gammar = 1;
> >
> > % Initial a LMI system
> > setlmis([]);
> >
> > % Define Variables
> >
> > % Q is a symmetric matrix, has a block size of 2 and
this
> > block is symmetric
> > Q = lmivar(1, [2 1]);
> >
> > % S1 a symmeric matrix, size 2 by 2
> > S1 = lmivar(1, [2 1]);
> >
> >
> > % S2 is 1 by 1 matrix
> > S2 = lmivar(1, [1 0]);
> >
> >
> > % Type of 2, size 1 by 2
> > M = lmivar(2, [1 2]);
> >
> >
> > %I use upper triangular to represent the LMI
> >
> > % pos in (1, 1)
> > lmiterm([1 1 1 Q], -1, 1);
> > lmiterm([1 1 1 S2], Bd, Bd');
> > lmiterm([1 1 1 S1], Ad, Ad');
> >
> > % pos (1, 2)
> > lmiterm([1 1 2 Q], A, 1);
> > lmiterm([1 1 2 M], B2, 1);
> >
> > % pos(1, 3)
> > lmiterm([1 1 3 0], B1);
> >
> > % pos(1, 4)
> > lmiterm([1 1 4 S2], Bd, Bd');
> > lmiterm([1 1 4 S1], Ad, Cd');
> >
> >
> > % pos(2, 2)
> > lmiterm([1 2 2 Q], -1, 1);
> >
> > % pos(2, 4)
> > lmiterm([1 2 4 Q], 1, C');
> >
> > lmiterm([1 2 4 -M], 1, D12');
> >
> > % pos(2, 5)
> > lmiterm([1 2 5 -M], 1, 1);
> >
> > % pos(2, 6)
> > lmiterm([1 2 6 Q], 1, 1);
> >
> > % pos(3, 3)
> > lmiterm([1 3 3 0], -(gammar^2));
> >
> > % pos(3, 4)
> > lmiterm([1 3 4 0], D11');
> >
> > % pos(4, 4)
> > lmiterm([1 4 4 0], -1);
> > lmiterm([1 4 4 S1], Cd, Cd');
> > lmiterm([1 4 4 S2], Dd, Dd');
> >
> > % pos(5, 5)
> > lmiterm([1 5 5 S2], -1, 1);
> >
> >
> > % pos(6, 6)
> > lmiterm([1 6 6 S1], -1, 1);
> >
> > lmis = getlmis;
> >
> > [tmin, feas] = feasp(lmis)
> >
> > --------------------------------
> > When I run it, I get error message:
> >
> > ??? Error using ==> lmiterm at 296
> > lhs of LMI #1, block (4,1): term dimensions
incompatible
> > with
> > other terms in same row
> >
> > Error in ==> paperor at 56
> > lmiterm([1 1 4 S1], Ad, Cd');
> >
> > I have checked many times and can't figure out why it
is
> > wrong, can anybody point it to me?
> >
>

Dear Johan:

Thank you very much. But I still have some doubts about
this.

You recommend me to use YALMIP, but I think the program you
write for me is not apply to me.

1.The original problem is for a discrete time linear delay
system which I have't write it here, If there exists
positive-define matrices Q, S1, S2 and a matrix M satisfied
that LMI, then we call it H-inf quadratically stable with H-
inf norm bound gammar. So I mean gammar cannot be a random
variable. So you write the program that object is to
minimize gamma^2, I think it is not suitable.

2.In my problem, matrices like A, Ad, Dd, they are all
specified, you use randn(n,n) to generate them. I replace
them with specified ones.

Re: LMI term dimensions incompatible

Johan Löfberg — Thu, 08 May 2008 12:20:19 -0400

"Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
<fvunbr$1tb$1@fred.mathworks.com>...
> "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> message <fvueq0$mf3$1@fred.mathworks.com>...
> > Well, I won't directly answer your question, but when I
> see
> > this, I can see that it must be annoying. My advice to you
> > is to use more modern tools to setup and solve the SDP.
> >
> > Using YALMIP and the solver SeDuMi
> > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php
> > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?
> n=Solvers.SEDUMI
> >
> > you would code your problem as below.
> >
> > I think this approach would save you a lot of agony during
> > the modelling.
> >
> > /johan
> >
> >
> > Q = sdpvar(n,n);
> > S1 = sdpvar(n,n);
> > S2 = sdpvar(n,n);
> >
> > gammasquared = sdpvar(1,1);
> >
> > A = randn(n,n);
> > Ad = randn(n,n);
> > Bd = randn(n,n);
> > B1 = randn(n,n);
> > B2 = randn(n,n);
> > M = randn(n,n);
> > Cd = randn(n,n);
> > C = randn(n,n);
> > D11 = randn(n,n);
> > D12 = randn(n,n);
> > Dd = randn(n,n);
> >
> >
> > % We could do something like this, but then we would have
> to
> > find out the
> > % dimensions of the zero blocks, and we are too lazy to
> do that
> > %B = [ -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M
> B1
> > Bd*S2*Dd'+Ad*S1*Cd' 0 0;
> > % Q*A'+M'*B2' -Q
> 0
> > Q*C'+M'*D12' M' Q;
> > % B1' 0 -
> gammasquared*I
> > D11' 0 0;
> > % Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M
> D11
> > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0;
> > % 0 M
> 0
> > 0 -S2 0;
> > % 0 Q
> 0
> > 0 0 -S1 ];
> >
> > % Instead, we use the blkvar shortcut. It automatically
> > fills in the blanks and symmetrizes for you
> > B = blkvar;
> > B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> > B(1,2) = A*Q+B2*M;
> > B(1,3) = B1;
> > B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> > B(2,2) = -Q;
> > B(2,4) = Q*C'+M'*D12';
> > B(2,5) = M';
> > B(2,6) = Q;
> > B(3,3) = -gammasquared*eye(size(B1,2));
> > B(3,4) = D11';
> > B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> > B(5,5) = -S2;
> > B(6,6) = -S1;
> >
> > % set up all constraints
> > Constraints = [B < 0, Q>0, S1>0, S2>0];
> > Objective = gammasquared;
> > % Minimize gamma^2
> > solvesdp(Constraints,Objective)
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> > <fvtuvp$aiv$1@fred.mathworks.com>...
> > > Is anyone can help me? I can figure out what happened
> to my
> > > programm.
> > >
> > > I need to solve a inequality:
> > >
> > > | -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
> > > | Q*A'+M'*B2' -Q 0
> > > | B1' 0 -gammar^2*I
> > > | Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
> > > | 0 M 0
> > > | 0 Q 0
> > >
> > > Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
> > > Q*C'+M'*D12' M' Q |
> > > D11' 0 0 | <0
> > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
> > > 0 -S2 0 |
> > > 0 0 -S1 |
> > >
> > > Matrices:Q, S1, S2 are positive-define.
> > >
> > > Below is programm:
> > > ===================================================
> > > A = [2 1; 0 1];
> > > Ad = [0.2 0.1; 0 0.1];
> > > B1 = [0.1 0.1]';
> > > B2 = [1 1]';
> > > Bd = [0.1 0.1]';
> > >
> > > C = [1, 1];
> > > Cd = [0.1, 0.1];
> > >
> > > D11 = 0.1;
> > > D12 = 1;
> > > Dd = 0.1;
> > >
> > > gammar = 1;
> > >
> > > % Initial a LMI system
> > > setlmis([]);
> > >
> > > % Define Variables
> > >
> > > % Q is a symmetric matrix, has a block size of 2 and
> this
> > > block is symmetric
> > > Q = lmivar(1, [2 1]);
> > >
> > > % S1 a symmeric matrix, size 2 by 2
> > > S1 = lmivar(1, [2 1]);
> > >
> > >
> > > % S2 is 1 by 1 matrix
> > > S2 = lmivar(1, [1 0]);
> > >
> > >
> > > % Type of 2, size 1 by 2
> > > M = lmivar(2, [1 2]);
> > >
> > >
> > > %I use upper triangular to represent the LMI
> > >
> > > % pos in (1, 1)
> > > lmiterm([1 1 1 Q], -1, 1);
> > > lmiterm([1 1 1 S2], Bd, Bd');
> > > lmiterm([1 1 1 S1], Ad, Ad');
> > >
> > > % pos (1, 2)
> > > lmiterm([1 1 2 Q], A, 1);
> > > lmiterm([1 1 2 M], B2, 1);
> > >
> > > % pos(1, 3)
> > > lmiterm([1 1 3 0], B1);
> > >
> > > % pos(1, 4)
> > > lmiterm([1 1 4 S2], Bd, Bd');
> > > lmiterm([1 1 4 S1], Ad, Cd');
> > >
> > >
> > > % pos(2, 2)
> > > lmiterm([1 2 2 Q], -1, 1);
> > >
> > > % pos(2, 4)
> > > lmiterm([1 2 4 Q], 1, C');
> > >
> > > lmiterm([1 2 4 -M], 1, D12');
> > >
> > > % pos(2, 5)
> > > lmiterm([1 2 5 -M], 1, 1);
> > >
> > > % pos(2, 6)
> > > lmiterm([1 2 6 Q], 1, 1);
> > >
> > > % pos(3, 3)
> > > lmiterm([1 3 3 0], -(gammar^2));
> > >
> > > % pos(3, 4)
> > > lmiterm([1 3 4 0], D11');
> > >
> > > % pos(4, 4)
> > > lmiterm([1 4 4 0], -1);
> > > lmiterm([1 4 4 S1], Cd, Cd');
> > > lmiterm([1 4 4 S2], Dd, Dd');
> > >
> > > % pos(5, 5)
> > > lmiterm([1 5 5 S2], -1, 1);
> > >
> > >
> > > % pos(6, 6)
> > > lmiterm([1 6 6 S1], -1, 1);
> > >
> > > lmis = getlmis;
> > >
> > > [tmin, feas] = feasp(lmis)
> > >
> > > --------------------------------
> > > When I run it, I get error message:
> > >
> > > ??? Error using ==> lmiterm at 296
> > > lhs of LMI #1, block (4,1): term dimensions
> incompatible
> > > with
> > > other terms in same row
> > >
> > > Error in ==> paperor at 56
> > > lmiterm([1 1 4 S1], Ad, Cd');
> > >
> > > I have checked many times and can't figure out why it
> is
> > > wrong, can anybody point it to me?
> > >
> >
>
> Dear Johan:
>
> Thank you very much. But I still have some doubts about
> this.
>
> You recommend me to use YALMIP, but I think the program you
> write for me is not apply to me.
>
> 1.The original problem is for a discrete time linear delay
> system which I have't write it here, If there exists
> positive-define matrices Q, S1, S2 and a matrix M satisfied
> that LMI, then we call it H-inf quadratically stable with H-
> inf norm bound gammar. So I mean gammar cannot be a random
> variable. So you write the program that object is to
> minimize gamma^2, I think it is not suitable.
>
> 2.In my problem, matrices like A, Ad, Dd, they are all
> specified, you use randn(n,n) to generate them. I replace
> them with specified ones.
>

I though gammar was a decision variable that you wanted to
optimize. If it is given, well then you just use that
instead and remove the objective from the call to solvesdp
and solve the feasibility problem instead

You can of course use your own data, I only defined random
matrices to get an example that was working.

The problem can be solved with YALMIP and SeDuMi without a
doubt, it is a trivial SDP problem.

Re: LMI term dimensions incompatible

Johan Löfberg — Thu, 08 May 2008 12:36:02 -0400

"Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
message <fvur63$oog$1@fred.mathworks.com>...
> "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> <fvunbr$1tb$1@fred.mathworks.com>...
> > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> > message <fvueq0$mf3$1@fred.mathworks.com>...
> > > Well, I won't directly answer your question, but when I
> > see
> > > this, I can see that it must be annoying. My advice to you
> > > is to use more modern tools to setup and solve the SDP.
> > >
> > > Using YALMIP and the solver SeDuMi
> > > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php
> > > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?
> > n=Solvers.SEDUMI
> > >
> > > you would code your problem as below.
> > >
> > > I think this approach would save you a lot of agony during
> > > the modelling.
> > >
> > > /johan
> > >
> > >
> > > Q = sdpvar(n,n);
> > > S1 = sdpvar(n,n);
> > > S2 = sdpvar(n,n);
> > >
> > > gammasquared = sdpvar(1,1);
> > >
> > > A = randn(n,n);
> > > Ad = randn(n,n);
> > > Bd = randn(n,n);
> > > B1 = randn(n,n);
> > > B2 = randn(n,n);
> > > M = randn(n,n);
> > > Cd = randn(n,n);
> > > C = randn(n,n);
> > > D11 = randn(n,n);
> > > D12 = randn(n,n);
> > > Dd = randn(n,n);
> > >
> > >
> > > % We could do something like this, but then we would have
> > to
> > > find out the
> > > % dimensions of the zero blocks, and we are too lazy to
> > do that
> > > %B = [ -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M
> > B1
> > > Bd*S2*Dd'+Ad*S1*Cd' 0 0;
> > > % Q*A'+M'*B2' -Q
> > 0
> > > Q*C'+M'*D12' M' Q;
> > > % B1' 0 -
> > gammasquared*I
> > > D11' 0 0;
> > > % Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M
> > D11
> > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0;
> > > % 0 M
> > 0
> > > 0 -S2 0;
> > > % 0 Q
> > 0
> > > 0 0 -S1 ];
> > >
> > > % Instead, we use the blkvar shortcut. It automatically
> > > fills in the blanks and symmetrizes for you
> > > B = blkvar;
> > > B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> > > B(1,2) = A*Q+B2*M;
> > > B(1,3) = B1;
> > > B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> > > B(2,2) = -Q;
> > > B(2,4) = Q*C'+M'*D12';
> > > B(2,5) = M';
> > > B(2,6) = Q;
> > > B(3,3) = -gammasquared*eye(size(B1,2));
> > > B(3,4) = D11';
> > > B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> > > B(5,5) = -S2;
> > > B(6,6) = -S1;
> > >
> > > % set up all constraints
> > > Constraints = [B < 0, Q>0, S1>0, S2>0];
> > > Objective = gammasquared;
> > > % Minimize gamma^2
> > > solvesdp(Constraints,Objective)
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > >
> > > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> > > <fvtuvp$aiv$1@fred.mathworks.com>...
> > > > Is anyone can help me? I can figure out what happened
> > to my
> > > > programm.
> > > >
> > > > I need to solve a inequality:
> > > >
> > > > | -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
> > > > | Q*A'+M'*B2' -Q 0
> > > > | B1' 0 -gammar^2*I
> > > > | Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
> > > > | 0 M 0
> > > > | 0 Q 0
> > > >
> > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
> > > > Q*C'+M'*D12' M' Q |
> > > > D11' 0 0 | <0
> > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
> > > > 0 -S2 0 |
> > > > 0 0 -S1 |
> > > >
> > > > Matrices:Q, S1, S2 are positive-define.
> > > >
> > > > Below is programm:
> > > > ===================================================
> > > > A = [2 1; 0 1];
> > > > Ad = [0.2 0.1; 0 0.1];
> > > > B1 = [0.1 0.1]';
> > > > B2 = [1 1]';
> > > > Bd = [0.1 0.1]';
> > > >
> > > > C = [1, 1];
> > > > Cd = [0.1, 0.1];
> > > >
> > > > D11 = 0.1;
> > > > D12 = 1;
> > > > Dd = 0.1;
> > > >
> > > > gammar = 1;
> > > >
> > > > % Initial a LMI system
> > > > setlmis([]);
> > > >
> > > > % Define Variables
> > > >
> > > > % Q is a symmetric matrix, has a block size of 2 and
> > this
> > > > block is symmetric
> > > > Q = lmivar(1, [2 1]);
> > > >
> > > > % S1 a symmeric matrix, size 2 by 2
> > > > S1 = lmivar(1, [2 1]);
> > > >
> > > >
> > > > % S2 is 1 by 1 matrix
> > > > S2 = lmivar(1, [1 0]);
> > > >
> > > >
> > > > % Type of 2, size 1 by 2
> > > > M = lmivar(2, [1 2]);
> > > >
> > > >
> > > > %I use upper triangular to represent the LMI
> > > >
> > > > % pos in (1, 1)
> > > > lmiterm([1 1 1 Q], -1, 1);
> > > > lmiterm([1 1 1 S2], Bd, Bd');
> > > > lmiterm([1 1 1 S1], Ad, Ad');
> > > >
> > > > % pos (1, 2)
> > > > lmiterm([1 1 2 Q], A, 1);
> > > > lmiterm([1 1 2 M], B2, 1);
> > > >
> > > > % pos(1, 3)
> > > > lmiterm([1 1 3 0], B1);
> > > >
> > > > % pos(1, 4)
> > > > lmiterm([1 1 4 S2], Bd, Bd');
> > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > >
> > > >
> > > > % pos(2, 2)
> > > > lmiterm([1 2 2 Q], -1, 1);
> > > >
> > > > % pos(2, 4)
> > > > lmiterm([1 2 4 Q], 1, C');
> > > >
> > > > lmiterm([1 2 4 -M], 1, D12');
> > > >
> > > > % pos(2, 5)
> > > > lmiterm([1 2 5 -M], 1, 1);
> > > >
> > > > % pos(2, 6)
> > > > lmiterm([1 2 6 Q], 1, 1);
> > > >
> > > > % pos(3, 3)
> > > > lmiterm([1 3 3 0], -(gammar^2));
> > > >
> > > > % pos(3, 4)
> > > > lmiterm([1 3 4 0], D11');
> > > >
> > > > % pos(4, 4)
> > > > lmiterm([1 4 4 0], -1);
> > > > lmiterm([1 4 4 S1], Cd, Cd');
> > > > lmiterm([1 4 4 S2], Dd, Dd');
> > > >
> > > > % pos(5, 5)
> > > > lmiterm([1 5 5 S2], -1, 1);
> > > >
> > > >
> > > > % pos(6, 6)
> > > > lmiterm([1 6 6 S1], -1, 1);
> > > >
> > > > lmis = getlmis;
> > > >
> > > > [tmin, feas] = feasp(lmis)
> > > >
> > > > --------------------------------
> > > > When I run it, I get error message:
> > > >
> > > > ??? Error using ==> lmiterm at 296
> > > > lhs of LMI #1, block (4,1): term dimensions
> > incompatible
> > > > with
> > > > other terms in same row
> > > >
> > > > Error in ==> paperor at 56
> > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > >
> > > > I have checked many times and can't figure out why it
> > is
> > > > wrong, can anybody point it to me?
> > > >
> > >
> >
> > Dear Johan:
> >
> > Thank you very much. But I still have some doubts about
> > this.
> >
> > You recommend me to use YALMIP, but I think the program you
> > write for me is not apply to me.
> >
> > 1.The original problem is for a discrete time linear delay
> > system which I have't write it here, If there exists
> > positive-define matrices Q, S1, S2 and a matrix M satisfied
> > that LMI, then we call it H-inf quadratically stable with H-
> > inf norm bound gammar. So I mean gammar cannot be a random
> > variable. So you write the program that object is to
> > minimize gamma^2, I think it is not suitable.
> >
> > 2.In my problem, matrices like A, Ad, Dd, they are all
> > specified, you use randn(n,n) to generate them. I replace
> > them with specified ones.
> >
>
>
> I though gammar was a decision variable that you wanted to
> optimize. If it is given, well then you just use that
> instead and remove the objective from the call to solvesdp
> and solve the feasibility problem instead
>
> You can of course use your own data, I only defined random
> matrices to get an example that was working.
>
> The problem can be solved with YALMIP and SeDuMi without a
> doubt, it is a trivial SDP problem.

..and I noticed you optimized over M too, so you should use

M = sdpvar(somesize,someothersize,'full')

Re: LMI term dimensions incompatible

Johan Löfberg — Thu, 08 May 2008 12:45:05 -0400

"Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
message <fvus3i$kci$1@fred.mathworks.com>...
> "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> message <fvur63$oog$1@fred.mathworks.com>...
> > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> > <fvunbr$1tb$1@fred.mathworks.com>...
> > > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> > > message <fvueq0$mf3$1@fred.mathworks.com>...
> > > > Well, I won't directly answer your question, but when I
> > > see
> > > > this, I can see that it must be annoying. My advice
to you
> > > > is to use more modern tools to setup and solve the SDP.
> > > >
> > > > Using YALMIP and the solver SeDuMi
> > > > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php
> > > > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?
> > > n=Solvers.SEDUMI
> > > >
> > > > you would code your problem as below.
> > > >
> > > > I think this approach would save you a lot of agony
during
> > > > the modelling.
> > > >
> > > > /johan
> > > >
> > > >
> > > > Q = sdpvar(n,n);
> > > > S1 = sdpvar(n,n);
> > > > S2 = sdpvar(n,n);
> > > >
> > > > gammasquared = sdpvar(1,1);
> > > >
> > > > A = randn(n,n);
> > > > Ad = randn(n,n);
> > > > Bd = randn(n,n);
> > > > B1 = randn(n,n);
> > > > B2 = randn(n,n);
> > > > M = randn(n,n);
> > > > Cd = randn(n,n);
> > > > C = randn(n,n);
> > > > D11 = randn(n,n);
> > > > D12 = randn(n,n);
> > > > Dd = randn(n,n);
> > > >
> > > >
> > > > % We could do something like this, but then we would
have
> > > to
> > > > find out the
> > > > % dimensions of the zero blocks, and we are too lazy to
> > > do that
> > > > %B = [ -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M
> > > B1
> > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0;
> > > > % Q*A'+M'*B2' -Q
> > > 0
> > > > Q*C'+M'*D12' M' Q;
> > > > % B1' 0 -
> > > gammasquared*I
> > > > D11' 0 0;
> > > > % Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M
> > > D11
> > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0;
> > > > % 0 M
> > > 0
> > > > 0 -S2 0;
> > > > % 0 Q
> > > 0
> > > > 0 0 -S1 ];
> > > >
> > > > % Instead, we use the blkvar shortcut. It automatically
> > > > fills in the blanks and symmetrizes for you
> > > > B = blkvar;
> > > > B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> > > > B(1,2) = A*Q+B2*M;
> > > > B(1,3) = B1;
> > > > B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> > > > B(2,2) = -Q;
> > > > B(2,4) = Q*C'+M'*D12';
> > > > B(2,5) = M';
> > > > B(2,6) = Q;
> > > > B(3,3) = -gammasquared*eye(size(B1,2));
> > > > B(3,4) = D11';
> > > > B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> > > > B(5,5) = -S2;
> > > > B(6,6) = -S1;
> > > >
> > > > % set up all constraints
> > > > Constraints = [B < 0, Q>0, S1>0, S2>0];
> > > > Objective = gammasquared;
> > > > % Minimize gamma^2
> > > > solvesdp(Constraints,Objective)
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > >
> > > > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> > > > <fvtuvp$aiv$1@fred.mathworks.com>...
> > > > > Is anyone can help me? I can figure out what happened
> > > to my
> > > > > programm.
> > > > >
> > > > > I need to solve a inequality:
> > > > >
> > > > > | -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
> > > > > | Q*A'+M'*B2' -Q 0
> > > > > | B1' 0 -gammar^2*I
> > > > > | Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
> > > > > | 0 M 0
> > > > > | 0 Q 0
> > > > >
> > > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
> > > > > Q*C'+M'*D12' M' Q |
> > > > > D11' 0 0 | <0
> > > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
> > > > > 0 -S2 0 |
> > > > > 0 0 -S1 |
> > > > >
> > > > > Matrices:Q, S1, S2 are positive-define.
> > > > >
> > > > > Below is programm:
> > > > > ===================================================
> > > > > A = [2 1; 0 1];
> > > > > Ad = [0.2 0.1; 0 0.1];
> > > > > B1 = [0.1 0.1]';
> > > > > B2 = [1 1]';
> > > > > Bd = [0.1 0.1]';
> > > > >
> > > > > C = [1, 1];
> > > > > Cd = [0.1, 0.1];
> > > > >
> > > > > D11 = 0.1;
> > > > > D12 = 1;
> > > > > Dd = 0.1;
> > > > >
> > > > > gammar = 1;
> > > > >
> > > > > % Initial a LMI system
> > > > > setlmis([]);
> > > > >
> > > > > % Define Variables
> > > > >
> > > > > % Q is a symmetric matrix, has a block size of 2 and
> > > this
> > > > > block is symmetric
> > > > > Q = lmivar(1, [2 1]);
> > > > >
> > > > > % S1 a symmeric matrix, size 2 by 2
> > > > > S1 = lmivar(1, [2 1]);
> > > > >
> > > > >
> > > > > % S2 is 1 by 1 matrix
> > > > > S2 = lmivar(1, [1 0]);
> > > > >
> > > > >
> > > > > % Type of 2, size 1 by 2
> > > > > M = lmivar(2, [1 2]);
> > > > >
> > > > >
> > > > > %I use upper triangular to represent the LMI
> > > > >
> > > > > % pos in (1, 1)
> > > > > lmiterm([1 1 1 Q], -1, 1);
> > > > > lmiterm([1 1 1 S2], Bd, Bd');
> > > > > lmiterm([1 1 1 S1], Ad, Ad');
> > > > >
> > > > > % pos (1, 2)
> > > > > lmiterm([1 1 2 Q], A, 1);
> > > > > lmiterm([1 1 2 M], B2, 1);
> > > > >
> > > > > % pos(1, 3)
> > > > > lmiterm([1 1 3 0], B1);
> > > > >
> > > > > % pos(1, 4)
> > > > > lmiterm([1 1 4 S2], Bd, Bd');
> > > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > > >
> > > > >
> > > > > % pos(2, 2)
> > > > > lmiterm([1 2 2 Q], -1, 1);
> > > > >
> > > > > % pos(2, 4)
> > > > > lmiterm([1 2 4 Q], 1, C');
> > > > >
> > > > > lmiterm([1 2 4 -M], 1, D12');
> > > > >
> > > > > % pos(2, 5)
> > > > > lmiterm([1 2 5 -M], 1, 1);
> > > > >
> > > > > % pos(2, 6)
> > > > > lmiterm([1 2 6 Q], 1, 1);
> > > > >
> > > > > % pos(3, 3)
> > > > > lmiterm([1 3 3 0], -(gammar^2));
> > > > >
> > > > > % pos(3, 4)
> > > > > lmiterm([1 3 4 0], D11');
> > > > >
> > > > > % pos(4, 4)
> > > > > lmiterm([1 4 4 0], -1);
> > > > > lmiterm([1 4 4 S1], Cd, Cd');
> > > > > lmiterm([1 4 4 S2], Dd, Dd');
> > > > >
> > > > > % pos(5, 5)
> > > > > lmiterm([1 5 5 S2], -1, 1);
> > > > >
> > > > >
> > > > > % pos(6, 6)
> > > > > lmiterm([1 6 6 S1], -1, 1);
> > > > >
> > > > > lmis = getlmis;
> > > > >
> > > > > [tmin, feas] = feasp(lmis)
> > > > >
> > > > > --------------------------------
> > > > > When I run it, I get error message:
> > > > >
> > > > > ??? Error using ==> lmiterm at 296
> > > > > lhs of LMI #1, block (4,1): term dimensions
> > > incompatible
> > > > > with
> > > > > other terms in same row
> > > > >
> > > > > Error in ==> paperor at 56
> > > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > > >
> > > > > I have checked many times and can't figure out why it
> > > is
> > > > > wrong, can anybody point it to me?
> > > > >
> > > >
> > >
> > > Dear Johan:
> > >
> > > Thank you very much. But I still have some doubts about
> > > this.
> > >
> > > You recommend me to use YALMIP, but I think the
program you
> > > write for me is not apply to me.
> > >
> > > 1.The original problem is for a discrete time linear
delay
> > > system which I have't write it here, If there exists
> > > positive-define matrices Q, S1, S2 and a matrix M
satisfied
> > > that LMI, then we call it H-inf quadratically stable
with H-
> > > inf norm bound gammar. So I mean gammar cannot be a
random
> > > variable. So you write the program that object is to
> > > minimize gamma^2, I think it is not suitable.
> > >
> > > 2.In my problem, matrices like A, Ad, Dd, they are all
> > > specified, you use randn(n,n) to generate them. I replace
> > > them with specified ones.
> > >
> >
> >
> > I though gammar was a decision variable that you wanted to
> > optimize. If it is given, well then you just use that
> > instead and remove the objective from the call to solvesdp
> > and solve the feasibility problem instead
> >
> > You can of course use your own data, I only defined random
> > matrices to get an example that was working.
> >
> > The problem can be solved with YALMIP and SeDuMi without a
> > doubt, it is a trivial SDP problem.
>
>
> ..and I noticed you optimized over M too, so you should use
>
> M = sdpvar(somesize,someothersize,'full')
>
>

To summarize

A = [2 1; 0 1];
Ad = [0.2 0.1; 0 0.1];
B1 = [0.1 0.1]';
B2 = [1 1]';
Bd = [0.1 0.1]';

C = [1, 1];
Cd = [0.1, 0.1];

D11 = 0.1;
D12 = 1;
Dd = 0.1;

gammar = 1;

Q = sdpvar(2,2);
S1 = sdpvar(2,2);
S2 = sdpvar(1);
% Full by definition, but just to rmember it if
% we change dimensions later
M = sdpvar(1,2,'full');

B = blkvar;
B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
B(1,2) = A*Q+B2*M;
B(1,3) = B1;
B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
B(2,2) = -Q;
B(2,4) = Q*C'+M'*D12';
B(2,5) = M';
B(2,6) = Q;
B(3,3) = -gammar^2*eye(size(B1,2));
B(3,4) = D11';
B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
B(5,5) = -S2;
B(6,6) = -S1;

% set up all constraints
Constraints = [B < 0, Q>0, S1>0, S2>0];
solvesdp(Constraints)
    yalmiptime: 0.3430
    solvertime: 1.3440
          info: 'No problems detected (SeDuMi-1.1)'
       problem: 0
        dimacs: [1.4589e-015 0 0 0 7.3848e-016 3.9007e-015]

>> double(Q)

ans =

    0.2425 -0.2091
   -0.2091 1.0081

>> double(S1)

ans =

    1.3613 -0.4978
   -0.4978 2.3019

>> double(S2)

ans =

    2.0517

>> double(M)

ans =

   -0.1367 -0.6933

Re: LMI term dimensions incompatible

Michael Zhang — Thu, 08 May 2008 14:28:04 -0400

"Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
message <fvuskh$mq9$1@fred.mathworks.com>...
> "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> message <fvus3i$kci$1@fred.mathworks.com>...
> > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> > message <fvur63$oog$1@fred.mathworks.com>...
> > > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> > > <fvunbr$1tb$1@fred.mathworks.com>...
> > > > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote
in
> > > > message <fvueq0$mf3$1@fred.mathworks.com>...
> > > > > Well, I won't directly answer your question, but
when I
> > > > see
> > > > > this, I can see that it must be annoying. My
advice
> to you
> > > > > is to use more modern tools to setup and solve
the SDP.
> > > > >
> > > > > Using YALMIP and the solver SeDuMi
> > > > > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php
> > > > > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?
> > > > n=Solvers.SEDUMI
> > > > >
> > > > > you would code your problem as below.
> > > > >
> > > > > I think this approach would save you a lot of
agony
> during
> > > > > the modelling.
> > > > >
> > > > > /johan
> > > > >
> > > > >
> > > > > Q = sdpvar(n,n);
> > > > > S1 = sdpvar(n,n);
> > > > > S2 = sdpvar(n,n);
> > > > >
> > > > > gammasquared = sdpvar(1,1);
> > > > >
> > > > > A = randn(n,n);
> > > > > Ad = randn(n,n);
> > > > > Bd = randn(n,n);
> > > > > B1 = randn(n,n);
> > > > > B2 = randn(n,n);
> > > > > M = randn(n,n);
> > > > > Cd = randn(n,n);
> > > > > C = randn(n,n);
> > > > > D11 = randn(n,n);
> > > > > D12 = randn(n,n);
> > > > > Dd = randn(n,n);
> > > > >
> > > > >
> > > > > % We could do something like this, but then we
would
> have
> > > > to
> > > > > find out the
> > > > > % dimensions of the zero blocks, and we are too
lazy to
> > > > do that
> > > > > %B = [ -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M
> > > > B1
> > > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0;
> > > > > % Q*A'+M'*B2' -Q
> > > > 0
> > > > > Q*C'+M'*D12' M' Q;
> > > > > % B1' 0 -
> > > > gammasquared*I
> > > > > D11' 0 0;
> > > > > % Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M
> > > > D11
> > > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0;
> > > > > % 0 M
> > > > 0
> > > > > 0 -S2 0;
> > > > > % 0 Q
> > > > 0
> > > > > 0 0 -S1 ];
> > > > >
> > > > > % Instead, we use the blkvar shortcut. It
automatically
> > > > > fills in the blanks and symmetrizes for you
> > > > > B = blkvar;
> > > > > B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> > > > > B(1,2) = A*Q+B2*M;
> > > > > B(1,3) = B1;
> > > > > B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> > > > > B(2,2) = -Q;
> > > > > B(2,4) = Q*C'+M'*D12';
> > > > > B(2,5) = M';
> > > > > B(2,6) = Q;
> > > > > B(3,3) = -gammasquared*eye(size(B1,2));
> > > > > B(3,4) = D11';
> > > > > B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> > > > > B(5,5) = -S2;
> > > > > B(6,6) = -S1;
> > > > >
> > > > > % set up all constraints
> > > > > Constraints = [B < 0, Q>0, S1>0, S2>0];
> > > > > Objective = gammasquared;
> > > > > % Minimize gamma^2
> > > > > solvesdp(Constraints,Objective)
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in
message
> > > > > <fvtuvp$aiv$1@fred.mathworks.com>...
> > > > > > Is anyone can help me? I can figure out what
happened
> > > > to my
> > > > > > programm.
> > > > > >
> > > > > > I need to solve a inequality:
> > > > > >
> > > > > > | -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
> > > > > > | Q*A'+M'*B2' -Q 0
> > > > > > | B1' 0 -gammar^2*I
> > > > > > | Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
> > > > > > | 0 M 0
> > > > > > | 0 Q 0
> > > > > >
> > > > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
> > > > > > Q*C'+M'*D12' M' Q |
> > > > > > D11' 0 0 | <0
> > > > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
> > > > > > 0 -S2 0 |
> > > > > > 0 0 -S1 |
> > > > > >
> > > > > > Matrices:Q, S1, S2 are positive-define.
> > > > > >
> > > > > > Below is programm:
> > > > > >
===================================================
> > > > > > A = [2 1; 0 1];
> > > > > > Ad = [0.2 0.1; 0 0.1];
> > > > > > B1 = [0.1 0.1]';
> > > > > > B2 = [1 1]';
> > > > > > Bd = [0.1 0.1]';
> > > > > >
> > > > > > C = [1, 1];
> > > > > > Cd = [0.1, 0.1];
> > > > > >
> > > > > > D11 = 0.1;
> > > > > > D12 = 1;
> > > > > > Dd = 0.1;
> > > > > >
> > > > > > gammar = 1;
> > > > > >
> > > > > > % Initial a LMI system
> > > > > > setlmis([]);
> > > > > >
> > > > > > % Define Variables
> > > > > >
> > > > > > % Q is a symmetric matrix, has a block size of
2 and
> > > > this
> > > > > > block is symmetric
> > > > > > Q = lmivar(1, [2 1]);
> > > > > >
> > > > > > % S1 a symmeric matrix, size 2 by 2
> > > > > > S1 = lmivar(1, [2 1]);
> > > > > >
> > > > > >
> > > > > > % S2 is 1 by 1 matrix
> > > > > > S2 = lmivar(1, [1 0]);
> > > > > >
> > > > > >
> > > > > > % Type of 2, size 1 by 2
> > > > > > M = lmivar(2, [1 2]);
> > > > > >
> > > > > >
> > > > > > %I use upper triangular to represent the LMI
> > > > > >
> > > > > > % pos in (1, 1)
> > > > > > lmiterm([1 1 1 Q], -1, 1);
> > > > > > lmiterm([1 1 1 S2], Bd, Bd');
> > > > > > lmiterm([1 1 1 S1], Ad, Ad');
> > > > > >
> > > > > > % pos (1, 2)
> > > > > > lmiterm([1 1 2 Q], A, 1);
> > > > > > lmiterm([1 1 2 M], B2, 1);
> > > > > >
> > > > > > % pos(1, 3)
> > > > > > lmiterm([1 1 3 0], B1);
> > > > > >
> > > > > > % pos(1, 4)
> > > > > > lmiterm([1 1 4 S2], Bd, Bd');
> > > > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > > > >
> > > > > >
> > > > > > % pos(2, 2)
> > > > > > lmiterm([1 2 2 Q], -1, 1);
> > > > > >
> > > > > > % pos(2, 4)
> > > > > > lmiterm([1 2 4 Q], 1, C');
> > > > > >
> > > > > > lmiterm([1 2 4 -M], 1, D12');
> > > > > >
> > > > > > % pos(2, 5)
> > > > > > lmiterm([1 2 5 -M], 1, 1);
> > > > > >
> > > > > > % pos(2, 6)
> > > > > > lmiterm([1 2 6 Q], 1, 1);
> > > > > >
> > > > > > % pos(3, 3)
> > > > > > lmiterm([1 3 3 0], -(gammar^2));
> > > > > >
> > > > > > % pos(3, 4)
> > > > > > lmiterm([1 3 4 0], D11');
> > > > > >
> > > > > > % pos(4, 4)
> > > > > > lmiterm([1 4 4 0], -1);
> > > > > > lmiterm([1 4 4 S1], Cd, Cd');
> > > > > > lmiterm([1 4 4 S2], Dd, Dd');
> > > > > >
> > > > > > % pos(5, 5)
> > > > > > lmiterm([1 5 5 S2], -1, 1);
> > > > > >
> > > > > >
> > > > > > % pos(6, 6)
> > > > > > lmiterm([1 6 6 S1], -1, 1);
> > > > > >
> > > > > > lmis = getlmis;
> > > > > >
> > > > > > [tmin, feas] = feasp(lmis)
> > > > > >
> > > > > > --------------------------------
> > > > > > When I run it, I get error message:
> > > > > >
> > > > > > ??? Error using ==> lmiterm at 296
> > > > > > lhs of LMI #1, block (4,1): term dimensions
> > > > incompatible
> > > > > > with
> > > > > > other terms in same row
> > > > > >
> > > > > > Error in ==> paperor at 56
> > > > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > > > >
> > > > > > I have checked many times and can't figure out
why it
> > > > is
> > > > > > wrong, can anybody point it to me?
> > > > > >
> > > > >
> > > >
> > > > Dear Johan:
> > > >
> > > > Thank you very much. But I still have some doubts
about
> > > > this.
> > > >
> > > > You recommend me to use YALMIP, but I think the
> program you
> > > > write for me is not apply to me.
> > > >
> > > > 1.The original problem is for a discrete time linear
> delay
> > > > system which I have't write it here, If there
exists
> > > > positive-define matrices Q, S1, S2 and a matrix M
> satisfied
> > > > that LMI, then we call it H-inf quadratically stable
> with H-
> > > > inf norm bound gammar. So I mean gammar cannot be a
> random
> > > > variable. So you write the program that object is
to
> > > > minimize gamma^2, I think it is not suitable.
> > > >
> > > > 2.In my problem, matrices like A, Ad, Dd, they are
all
> > > > specified, you use randn(n,n) to generate them. I
replace
> > > > them with specified ones.
> > > >
> > >
> > >
> > > I though gammar was a decision variable that you
wanted to
> > > optimize. If it is given, well then you just use that
> > > instead and remove the objective from the call to
solvesdp
> > > and solve the feasibility problem instead
> > >
> > > You can of course use your own data, I only defined
random
> > > matrices to get an example that was working.
> > >
> > > The problem can be solved with YALMIP and SeDuMi
without a
> > > doubt, it is a trivial SDP problem.
> >
> >
> > ..and I noticed you optimized over M too, so you should
use
> >
> > M = sdpvar(somesize,someothersize,'full')
> >
> >
>
> To summarize
>
> A = [2 1; 0 1];
> Ad = [0.2 0.1; 0 0.1];
> B1 = [0.1 0.1]';
> B2 = [1 1]';
> Bd = [0.1 0.1]';
>
> C = [1, 1];
> Cd = [0.1, 0.1];
>
> D11 = 0.1;
> D12 = 1;
> Dd = 0.1;
>
> gammar = 1;
>
> Q = sdpvar(2,2);
> S1 = sdpvar(2,2);
> S2 = sdpvar(1);
> % Full by definition, but just to rmember it if
> % we change dimensions later
> M = sdpvar(1,2,'full');
>
> B = blkvar;
> B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> B(1,2) = A*Q+B2*M;
> B(1,3) = B1;
> B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> B(2,2) = -Q;
> B(2,4) = Q*C'+M'*D12';
> B(2,5) = M';
> B(2,6) = Q;
> B(3,3) = -gammar^2*eye(size(B1,2));
> B(3,4) = D11';
> B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> B(5,5) = -S2;
> B(6,6) = -S1;
>
> % set up all constraints
> Constraints = [B < 0, Q>0, S1>0, S2>0];
> solvesdp(Constraints)
> yalmiptime: 0.3430
> solvertime: 1.3440
> info: 'No problems detected (SeDuMi-1.1)'
> problem: 0
> dimacs: [1.4589e-015 0 0 0 7.3848e-016 3.9007e-
015]
>
>
> >> double(Q)
>
> ans =
>
> 0.2425 -0.2091
> -0.2091 1.0081
>
> >> double(S1)
>
> ans =
>
> 1.3613 -0.4978
> -0.4978 2.3019
>
> >> double(S2)
>
> ans =
>
> 2.0517
>
> >> double(M)
>
> ans =
>
> -0.1367 -0.6933
>
>
>
This LMI example is what I read from a paper, but the
author's result is different form yours. And he gave
proofs, I think the author only use matlab and we use other
toolboxes. I doubt if there really exists result difference
because of toolboxes?

The paper's address is http://www.sciencedirect.com/science?
_ob=ArticleURL&_udi=B6V21-3WWV8W6-B&_user=10&_coverDate=08%
2F31%
2F1999&_alid=736573613&_rdoc=1&_fmt=high&_orig=search&_cdi=5
689&_sort=d&_docanchor=&view=c&_ct=1&_acct=C000050221&_versi
on=1&_urlVersion=0&_userid=10&md5=8ecef13fb66b50ddc4a3990637
4c61b7

Re: LMI term dimensions incompatible

Johan Löfberg — Thu, 08 May 2008 14:38:04 -0400

"Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
<fvv2lk$lua$1@fred.mathworks.com>...
> "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> message <fvuskh$mq9$1@fred.mathworks.com>...
> > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> > message <fvus3i$kci$1@fred.mathworks.com>...
> > > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> > > message <fvur63$oog$1@fred.mathworks.com>...
> > > > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> > > > <fvunbr$1tb$1@fred.mathworks.com>...
> > > > > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote
> in
> > > > > message <fvueq0$mf3$1@fred.mathworks.com>...
> > > > > > Well, I won't directly answer your question, but
> when I
> > > > > see
> > > > > > this, I can see that it must be annoying. My
> advice
> > to you
> > > > > > is to use more modern tools to setup and solve
> the SDP.
> > > > > >
> > > > > > Using YALMIP and the solver SeDuMi
> > > > > > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php
> > > > > > http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?
> > > > > n=Solvers.SEDUMI
> > > > > >
> > > > > > you would code your problem as below.
> > > > > >
> > > > > > I think this approach would save you a lot of
> agony
> > during
> > > > > > the modelling.
> > > > > >
> > > > > > /johan
> > > > > >
> > > > > >
> > > > > > Q = sdpvar(n,n);
> > > > > > S1 = sdpvar(n,n);
> > > > > > S2 = sdpvar(n,n);
> > > > > >
> > > > > > gammasquared = sdpvar(1,1);
> > > > > >
> > > > > > A = randn(n,n);
> > > > > > Ad = randn(n,n);
> > > > > > Bd = randn(n,n);
> > > > > > B1 = randn(n,n);
> > > > > > B2 = randn(n,n);
> > > > > > M = randn(n,n);
> > > > > > Cd = randn(n,n);
> > > > > > C = randn(n,n);
> > > > > > D11 = randn(n,n);
> > > > > > D12 = randn(n,n);
> > > > > > Dd = randn(n,n);
> > > > > >
> > > > > >
> > > > > > % We could do something like this, but then we
> would
> > have
> > > > > to
> > > > > > find out the
> > > > > > % dimensions of the zero blocks, and we are too
> lazy to
> > > > > do that
> > > > > > %B = [ -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M
> > > > > B1
> > > > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0;
> > > > > > % Q*A'+M'*B2' -Q
> > > > > 0
> > > > > > Q*C'+M'*D12' M' Q;
> > > > > > % B1' 0 -
> > > > > gammasquared*I
> > > > > > D11' 0 0;
> > > > > > % Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M
> > > > > D11
> > > > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0;
> > > > > > % 0 M
> > > > > 0
> > > > > > 0 -S2 0;
> > > > > > % 0 Q
> > > > > 0
> > > > > > 0 0 -S1 ];
> > > > > >
> > > > > > % Instead, we use the blkvar shortcut. It
> automatically
> > > > > > fills in the blanks and symmetrizes for you
> > > > > > B = blkvar;
> > > > > > B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> > > > > > B(1,2) = A*Q+B2*M;
> > > > > > B(1,3) = B1;
> > > > > > B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> > > > > > B(2,2) = -Q;
> > > > > > B(2,4) = Q*C'+M'*D12';
> > > > > > B(2,5) = M';
> > > > > > B(2,6) = Q;
> > > > > > B(3,3) = -gammasquared*eye(size(B1,2));
> > > > > > B(3,4) = D11';
> > > > > > B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> > > > > > B(5,5) = -S2;
> > > > > > B(6,6) = -S1;
> > > > > >
> > > > > > % set up all constraints
> > > > > > Constraints = [B < 0, Q>0, S1>0, S2>0];
> > > > > > Objective = gammasquared;
> > > > > > % Minimize gamma^2
> > > > > > solvesdp(Constraints,Objective)
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in
> message
> > > > > > <fvtuvp$aiv$1@fred.mathworks.com>...
> > > > > > > Is anyone can help me? I can figure out what
> happened
> > > > > to my
> > > > > > > programm.
> > > > > > >
> > > > > > > I need to solve a inequality:
> > > > > > >
> > > > > > > | -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
> > > > > > > | Q*A'+M'*B2' -Q 0
> > > > > > > | B1' 0 -gammar^2*I
> > > > > > > | Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
> > > > > > > | 0 M 0
> > > > > > > | 0 Q 0
> > > > > > >
> > > > > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
> > > > > > > Q*C'+M'*D12' M' Q |
> > > > > > > D11' 0 0 | <0
> > > > > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
> > > > > > > 0 -S2 0 |
> > > > > > > 0 0 -S1 |
> > > > > > >
> > > > > > > Matrices:Q, S1, S2 are positive-define.
> > > > > > >
> > > > > > > Below is programm:
> > > > > > >
> ===================================================
> > > > > > > A = [2 1; 0 1];
> > > > > > > Ad = [0.2 0.1; 0 0.1];
> > > > > > > B1 = [0.1 0.1]';
> > > > > > > B2 = [1 1]';
> > > > > > > Bd = [0.1 0.1]';
> > > > > > >
> > > > > > > C = [1, 1];
> > > > > > > Cd = [0.1, 0.1];
> > > > > > >
> > > > > > > D11 = 0.1;
> > > > > > > D12 = 1;
> > > > > > > Dd = 0.1;
> > > > > > >
> > > > > > > gammar = 1;
> > > > > > >
> > > > > > > % Initial a LMI system
> > > > > > > setlmis([]);
> > > > > > >
> > > > > > > % Define Variables
> > > > > > >
> > > > > > > % Q is a symmetric matrix, has a block size of
> 2 and
> > > > > this
> > > > > > > block is symmetric
> > > > > > > Q = lmivar(1, [2 1]);
> > > > > > >
> > > > > > > % S1 a symmeric matrix, size 2 by 2
> > > > > > > S1 = lmivar(1, [2 1]);
> > > > > > >
> > > > > > >
> > > > > > > % S2 is 1 by 1 matrix
> > > > > > > S2 = lmivar(1, [1 0]);
> > > > > > >
> > > > > > >
> > > > > > > % Type of 2, size 1 by 2
> > > > > > > M = lmivar(2, [1 2]);
> > > > > > >
> > > > > > >
> > > > > > > %I use upper triangular to represent the LMI
> > > > > > >
> > > > > > > % pos in (1, 1)
> > > > > > > lmiterm([1 1 1 Q], -1, 1);
> > > > > > > lmiterm([1 1 1 S2], Bd, Bd');
> > > > > > > lmiterm([1 1 1 S1], Ad, Ad');
> > > > > > >
> > > > > > > % pos (1, 2)
> > > > > > > lmiterm([1 1 2 Q], A, 1);
> > > > > > > lmiterm([1 1 2 M], B2, 1);
> > > > > > >
> > > > > > > % pos(1, 3)
> > > > > > > lmiterm([1 1 3 0], B1);
> > > > > > >
> > > > > > > % pos(1, 4)
> > > > > > > lmiterm([1 1 4 S2], Bd, Bd');
> > > > > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > > > > >
> > > > > > >
> > > > > > > % pos(2, 2)
> > > > > > > lmiterm([1 2 2 Q], -1, 1);
> > > > > > >
> > > > > > > % pos(2, 4)
> > > > > > > lmiterm([1 2 4 Q], 1, C');
> > > > > > >
> > > > > > > lmiterm([1 2 4 -M], 1, D12');
> > > > > > >
> > > > > > > % pos(2, 5)
> > > > > > > lmiterm([1 2 5 -M], 1, 1);
> > > > > > >
> > > > > > > % pos(2, 6)
> > > > > > > lmiterm([1 2 6 Q], 1, 1);
> > > > > > >
> > > > > > > % pos(3, 3)
> > > > > > > lmiterm([1 3 3 0], -(gammar^2));
> > > > > > >
> > > > > > > % pos(3, 4)
> > > > > > > lmiterm([1 3 4 0], D11');
> > > > > > >
> > > > > > > % pos(4, 4)
> > > > > > > lmiterm([1 4 4 0], -1);
> > > > > > > lmiterm([1 4 4 S1], Cd, Cd');
> > > > > > > lmiterm([1 4 4 S2], Dd, Dd');
> > > > > > >
> > > > > > > % pos(5, 5)
> > > > > > > lmiterm([1 5 5 S2], -1, 1);
> > > > > > >
> > > > > > >
> > > > > > > % pos(6, 6)
> > > > > > > lmiterm([1 6 6 S1], -1, 1);
> > > > > > >
> > > > > > > lmis = getlmis;
> > > > > > >
> > > > > > > [tmin, feas] = feasp(lmis)
> > > > > > >
> > > > > > > --------------------------------
> > > > > > > When I run it, I get error message:
> > > > > > >
> > > > > > > ??? Error using ==> lmiterm at 296
> > > > > > > lhs of LMI #1, block (4,1): term dimensions
> > > > > incompatible
> > > > > > > with
> > > > > > > other terms in same row
> > > > > > >
> > > > > > > Error in ==> paperor at 56
> > > > > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > > > > >
> > > > > > > I have checked many times and can't figure out
> why it
> > > > > is
> > > > > > > wrong, can anybody point it to me?
> > > > > > >
> > > > > >
> > > > >
> > > > > Dear Johan:
> > > > >
> > > > > Thank you very much. But I still have some doubts
> about
> > > > > this.
> > > > >
> > > > > You recommend me to use YALMIP, but I think the
> > program you
> > > > > write for me is not apply to me.
> > > > >
> > > > > 1.The original problem is for a discrete time linear
> > delay
> > > > > system which I have't write it here, If there
> exists
> > > > > positive-define matrices Q, S1, S2 and a matrix M
> > satisfied
> > > > > that LMI, then we call it H-inf quadratically stable
> > with H-
> > > > > inf norm bound gammar. So I mean gammar cannot be a
> > random
> > > > > variable. So you write the program that object is
> to
> > > > > minimize gamma^2, I think it is not suitable.
> > > > >
> > > > > 2.In my problem, matrices like A, Ad, Dd, they are
> all
> > > > > specified, you use randn(n,n) to generate them. I
> replace
> > > > > them with specified ones.
> > > > >
> > > >
> > > >
> > > > I though gammar was a decision variable that you
> wanted to
> > > > optimize. If it is given, well then you just use that
> > > > instead and remove the objective from the call to
> solvesdp
> > > > and solve the feasibility problem instead
> > > >
> > > > You can of course use your own data, I only defined
> random
> > > > matrices to get an example that was working.
> > > >
> > > > The problem can be solved with YALMIP and SeDuMi
> without a
> > > > doubt, it is a trivial SDP problem.
> > >
> > >
> > > ..and I noticed you optimized over M too, so you should
> use
> > >
> > > M = sdpvar(somesize,someothersize,'full')
> > >
> > >
> >
> > To summarize
> >
> > A = [2 1; 0 1];
> > Ad = [0.2 0.1; 0 0.1];
> > B1 = [0.1 0.1]';
> > B2 = [1 1]';
> > Bd = [0.1 0.1]';
> >
> > C = [1, 1];
> > Cd = [0.1, 0.1];
> >
> > D11 = 0.1;
> > D12 = 1;
> > Dd = 0.1;
> >
> > gammar = 1;
> >
> > Q = sdpvar(2,2);
> > S1 = sdpvar(2,2);
> > S2 = sdpvar(1);
> > % Full by definition, but just to rmember it if
> > % we change dimensions later
> > M = sdpvar(1,2,'full');
> >
> > B = blkvar;
> > B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> > B(1,2) = A*Q+B2*M;
> > B(1,3) = B1;
> > B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> > B(2,2) = -Q;
> > B(2,4) = Q*C'+M'*D12';
> > B(2,5) = M';
> > B(2,6) = Q;
> > B(3,3) = -gammar^2*eye(size(B1,2));
> > B(3,4) = D11';
> > B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> > B(5,5) = -S2;
> > B(6,6) = -S1;
> >
> > % set up all constraints
> > Constraints = [B < 0, Q>0, S1>0, S2>0];
> > solvesdp(Constraints)
> > yalmiptime: 0.3430
> > solvertime: 1.3440
> > info: 'No problems detected (SeDuMi-1.1)'
> > problem: 0
> > dimacs: [1.4589e-015 0 0 0 7.3848e-016 3.9007e-
> 015]
> >
> >
> > >> double(Q)
> >
> > ans =
> >
> > 0.2425 -0.2091
> > -0.2091 1.0081
> >
> > >> double(S1)
> >
> > ans =
> >
> > 1.3613 -0.4978
> > -0.4978 2.3019
> >
> > >> double(S2)
> >
> > ans =
> >
> > 2.0517
> >
> > >> double(M)
> >
> > ans =
> >
> > -0.1367 -0.6933
> >
> >
> >
> This LMI example is what I read from a paper, but the
> author's result is different form yours. And he gave
> proofs, I think the author only use matlab and we use other
> toolboxes. I doubt if there really exists result difference
> because of toolboxes?
>
> The paper's address is http://www.sciencedirect.com/science?
> _ob=ArticleURL&_udi=B6V21-3WWV8W6-B&_user=10&_coverDate=08%
> 2F31%
> 2F1999&_alid=736573613&_rdoc=1&_fmt=high&_orig=search&_cdi=5
> 689&_sort=d&_docanchor=&view=c&_ct=1&_acct=C000050221&_versi
> on=1&_urlVersion=0&_userid=10&md5=8ecef13fb66b50ddc4a3990637
> 4c61b7

The solution is not unique since you only solve a
feasibility problem

Re: LMI term dimensions incompatible

Michael Zhang — Fri, 09 May 2008 01:07:06 -0400

"Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
message <fvv38c$sug$1@fred.mathworks.com>...
> "Michael Zhang" <cy_xiaoxiao@126.com> wrote in message
> <fvv2lk$lua$1@fred.mathworks.com>...
> > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> > message <fvuskh$mq9$1@fred.mathworks.com>...
> > > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote in
> > > message <fvus3i$kci$1@fred.mathworks.com>...
> > > > "Johan L?fberg" <loefberg@control.ee.ethz.ch> wrote
in
> > > > message <fvur63$oog$1@fred.mathworks.com>...
> > > > > "Michael Zhang" <cy_xiaoxiao@126.com> wrote in
message
> > > > > <fvunbr$1tb$1@fred.mathworks.com>...
> > > > > > "Johan L?fberg" <loefberg@control.ee.ethz.ch>
wrote
> > in
> > > > > > message <fvueq0$mf3$1@fred.mathworks.com>...
> > > > > > > Well, I won't directly answer your question,
but
> > when I
> > > > > > see
> > > > > > > this, I can see that it must be annoying. My
> > advice
> > > to you
> > > > > > > is to use more modern tools to setup and
solve
> > the SDP.
> > > > > > >
> > > > > > > Using YALMIP and the solver SeDuMi
> > > > > > >
http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php
> > > > > > >
http://control.ee.ethz.ch/~joloef/wiki/pmwiki.php?
> > > > > > n=Solvers.SEDUMI
> > > > > > >
> > > > > > > you would code your problem as below.
> > > > > > >
> > > > > > > I think this approach would save you a lot of
> > agony
> > > during
> > > > > > > the modelling.
> > > > > > >
> > > > > > > /johan
> > > > > > >
> > > > > > >
> > > > > > > Q = sdpvar(n,n);
> > > > > > > S1 = sdpvar(n,n);
> > > > > > > S2 = sdpvar(n,n);
> > > > > > >
> > > > > > > gammasquared = sdpvar(1,1);
> > > > > > >
> > > > > > > A = randn(n,n);
> > > > > > > Ad = randn(n,n);
> > > > > > > Bd = randn(n,n);
> > > > > > > B1 = randn(n,n);
> > > > > > > B2 = randn(n,n);
> > > > > > > M = randn(n,n);
> > > > > > > Cd = randn(n,n);
> > > > > > > C = randn(n,n);
> > > > > > > D11 = randn(n,n);
> > > > > > > D12 = randn(n,n);
> > > > > > > Dd = randn(n,n);
> > > > > > >
> > > > > > >
> > > > > > > % We could do something like this, but then
we
> > would
> > > have
> > > > > > to
> > > > > > > find out the
> > > > > > > % dimensions of the zero blocks, and we are
too
> > lazy to
> > > > > > do that
> > > > > > > %B = [ -Q+Bd*S2*Bd'+Ad*S1*Ad'
A*Q+B2*M
> > > > > > B1
> > > > > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0;
> > > > > > > % Q*A'+M'*B2' -Q
> > > > > > 0
> > > > > > > Q*C'+M'*D12' M' Q;
> > > > > > > % B1' 0 -
> > > > > > gammasquared*I
> > > > > > > D11' 0 0;
> > > > > > > % Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M
> > > > > > D11
> > > > > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0;
> > > > > > > % 0 M
> > > > > > 0
> > > > > > > 0 -S2 0;
> > > > > > > % 0 Q
> > > > > > 0
> > > > > > > 0 0 -S1 ];
> > > > > > >
> > > > > > > % Instead, we use the blkvar shortcut. It
> > automatically
> > > > > > > fills in the blanks and symmetrizes for you
> > > > > > > B = blkvar;
> > > > > > > B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> > > > > > > B(1,2) = A*Q+B2*M;
> > > > > > > B(1,3) = B1;
> > > > > > > B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> > > > > > > B(2,2) = -Q;
> > > > > > > B(2,4) = Q*C'+M'*D12';
> > > > > > > B(2,5) = M';
> > > > > > > B(2,6) = Q;
> > > > > > > B(3,3) = -gammasquared*eye(size(B1,2));
> > > > > > > B(3,4) = D11';
> > > > > > > B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> > > > > > > B(5,5) = -S2;
> > > > > > > B(6,6) = -S1;
> > > > > > >
> > > > > > > % set up all constraints
> > > > > > > Constraints = [B < 0, Q>0, S1>0, S2>0];
> > > > > > > Objective = gammasquared;
> > > > > > > % Minimize gamma^2
> > > > > > > solvesdp(Constraints,Objective)
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > "Michael Zhang" <cy_xiaoxiao@126.com> wrote
in
> > message
> > > > > > > <fvtuvp$aiv$1@fred.mathworks.com>...
> > > > > > > > Is anyone can help me? I can figure out
what
> > happened
> > > > > > to my
> > > > > > > > programm.
> > > > > > > >
> > > > > > > > I need to solve a inequality:
> > > > > > > >
> > > > > > > > | -Q+Bd*S2*Bd'+Ad*S1*Ad' A*Q+B2*M B1
> > > > > > > > | Q*A'+M'*B2' -Q 0
> > > > > > > > | B1' 0 -
gammar^2*I
> > > > > > > > | Dd*S2*Bd'+Cd*S1*Ad' C*Q+D12*M D11
> > > > > > > > | 0 M 0
> > > > > > > > | 0 Q 0
> > > > > > > >
> > > > > > > > Bd*S2*Dd'+Ad*S1*Cd' 0 0 |
> > > > > > > > Q*C'+M'*D12' M' Q |
> > > > > > > > D11' 0 0 | <0
> > > > > > > > -I+Cd*S1*Cd'+Dd*S2*Dd' 0 0 |
> > > > > > > > 0 -S2 0 |
> > > > > > > > 0 0 -S1 |
> > > > > > > >
> > > > > > > > Matrices:Q, S1, S2 are positive-define.
> > > > > > > >
> > > > > > > > Below is programm:
> > > > > > > >
> > ===================================================
> > > > > > > > A = [2 1; 0 1];
> > > > > > > > Ad = [0.2 0.1; 0 0.1];
> > > > > > > > B1 = [0.1 0.1]';
> > > > > > > > B2 = [1 1]';
> > > > > > > > Bd = [0.1 0.1]';
> > > > > > > >
> > > > > > > > C = [1, 1];
> > > > > > > > Cd = [0.1, 0.1];
> > > > > > > >
> > > > > > > > D11 = 0.1;
> > > > > > > > D12 = 1;
> > > > > > > > Dd = 0.1;
> > > > > > > >
> > > > > > > > gammar = 1;
> > > > > > > >
> > > > > > > > % Initial a LMI system
> > > > > > > > setlmis([]);
> > > > > > > >
> > > > > > > > % Define Variables
> > > > > > > >
> > > > > > > > % Q is a symmetric matrix, has a block size
of
> > 2 and
> > > > > > this
> > > > > > > > block is symmetric
> > > > > > > > Q = lmivar(1, [2 1]);
> > > > > > > >
> > > > > > > > % S1 a symmeric matrix, size 2 by 2
> > > > > > > > S1 = lmivar(1, [2 1]);
> > > > > > > >
> > > > > > > >
> > > > > > > > % S2 is 1 by 1 matrix
> > > > > > > > S2 = lmivar(1, [1 0]);
> > > > > > > >
> > > > > > > >
> > > > > > > > % Type of 2, size 1 by 2
> > > > > > > > M = lmivar(2, [1 2]);
> > > > > > > >
> > > > > > > >
> > > > > > > > %I use upper triangular to represent the LMI
> > > > > > > >
> > > > > > > > % pos in (1, 1)
> > > > > > > > lmiterm([1 1 1 Q], -1, 1);
> > > > > > > > lmiterm([1 1 1 S2], Bd, Bd');
> > > > > > > > lmiterm([1 1 1 S1], Ad, Ad');
> > > > > > > >
> > > > > > > > % pos (1, 2)
> > > > > > > > lmiterm([1 1 2 Q], A, 1);
> > > > > > > > lmiterm([1 1 2 M], B2, 1);
> > > > > > > >
> > > > > > > > % pos(1, 3)
> > > > > > > > lmiterm([1 1 3 0], B1);
> > > > > > > >
> > > > > > > > % pos(1, 4)
> > > > > > > > lmiterm([1 1 4 S2], Bd, Bd');
> > > > > > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > > > > > >
> > > > > > > >
> > > > > > > > % pos(2, 2)
> > > > > > > > lmiterm([1 2 2 Q], -1, 1);
> > > > > > > >
> > > > > > > > % pos(2, 4)
> > > > > > > > lmiterm([1 2 4 Q], 1, C');
> > > > > > > >
> > > > > > > > lmiterm([1 2 4 -M], 1, D12');
> > > > > > > >
> > > > > > > > % pos(2, 5)
> > > > > > > > lmiterm([1 2 5 -M], 1, 1);
> > > > > > > >
> > > > > > > > % pos(2, 6)
> > > > > > > > lmiterm([1 2 6 Q], 1, 1);
> > > > > > > >
> > > > > > > > % pos(3, 3)
> > > > > > > > lmiterm([1 3 3 0], -(gammar^2));
> > > > > > > >
> > > > > > > > % pos(3, 4)
> > > > > > > > lmiterm([1 3 4 0], D11');
> > > > > > > >
> > > > > > > > % pos(4, 4)
> > > > > > > > lmiterm([1 4 4 0], -1);
> > > > > > > > lmiterm([1 4 4 S1], Cd, Cd');
> > > > > > > > lmiterm([1 4 4 S2], Dd, Dd');
> > > > > > > >
> > > > > > > > % pos(5, 5)
> > > > > > > > lmiterm([1 5 5 S2], -1, 1);
> > > > > > > >
> > > > > > > >
> > > > > > > > % pos(6, 6)
> > > > > > > > lmiterm([1 6 6 S1], -1, 1);
> > > > > > > >
> > > > > > > > lmis = getlmis;
> > > > > > > >
> > > > > > > > [tmin, feas] = feasp(lmis)
> > > > > > > >
> > > > > > > > --------------------------------
> > > > > > > > When I run it, I get error message:
> > > > > > > >
> > > > > > > > ??? Error using ==> lmiterm at 296
> > > > > > > > lhs of LMI #1, block (4,1): term dimensions
> > > > > > incompatible
> > > > > > > > with
> > > > > > > > other terms in same row
> > > > > > > >
> > > > > > > > Error in ==> paperor at 56
> > > > > > > > lmiterm([1 1 4 S1], Ad, Cd');
> > > > > > > >
> > > > > > > > I have checked many times and can't figure
out
> > why it
> > > > > > is
> > > > > > > > wrong, can anybody point it to me?
> > > > > > > >
> > > > > > >
> > > > > >
> > > > > > Dear Johan:
> > > > > >
> > > > > > Thank you very much. But I still have some
doubts
> > about
> > > > > > this.
> > > > > >
> > > > > > You recommend me to use YALMIP, but I think the
> > > program you
> > > > > > write for me is not apply to me.
> > > > > >
> > > > > > 1.The original problem is for a discrete time
linear
> > > delay
> > > > > > system which I have't write it here, If there
> > exists
> > > > > > positive-define matrices Q, S1, S2 and a matrix
M
> > > satisfied
> > > > > > that LMI, then we call it H-inf quadratically
stable
> > > with H-
> > > > > > inf norm bound gammar. So I mean gammar cannot
be a
> > > random
> > > > > > variable. So you write the program that object
is
> > to
> > > > > > minimize gamma^2, I think it is not suitable.
> > > > > >
> > > > > > 2.In my problem, matrices like A, Ad, Dd, they
are
> > all
> > > > > > specified, you use randn(n,n) to generate them.
I
> > replace
> > > > > > them with specified ones.
> > > > > >
> > > > >
> > > > >
> > > > > I though gammar was a decision variable that you
> > wanted to
> > > > > optimize. If it is given, well then you just use
that
> > > > > instead and remove the objective from the call to
> > solvesdp
> > > > > and solve the feasibility problem instead
> > > > >
> > > > > You can of course use your own data, I only
defined
> > random
> > > > > matrices to get an example that was working.
> > > > >
> > > > > The problem can be solved with YALMIP and SeDuMi
> > without a
> > > > > doubt, it is a trivial SDP problem.
> > > >
> > > >
> > > > ..and I noticed you optimized over M too, so you
should
> > use
> > > >
> > > > M = sdpvar(somesize,someothersize,'full')
> > > >
> > > >
> > >
> > > To summarize
> > >
> > > A = [2 1; 0 1];
> > > Ad = [0.2 0.1; 0 0.1];
> > > B1 = [0.1 0.1]';
> > > B2 = [1 1]';
> > > Bd = [0.1 0.1]';
> > >
> > > C = [1, 1];
> > > Cd = [0.1, 0.1];
> > >
> > > D11 = 0.1;
> > > D12 = 1;
> > > Dd = 0.1;
> > >
> > > gammar = 1;
> > >
> > > Q = sdpvar(2,2);
> > > S1 = sdpvar(2,2);
> > > S2 = sdpvar(1);
> > > % Full by definition, but just to rmember it if
> > > % we change dimensions later
> > > M = sdpvar(1,2,'full');
> > >
> > > B = blkvar;
> > > B(1,1) = -Q+Bd*S2*Bd'+Ad*S1*Ad';
> > > B(1,2) = A*Q+B2*M;
> > > B(1,3) = B1;
> > > B(1,4) = Bd*S2*Dd'+Ad*S1*Cd';
> > > B(2,2) = -Q;
> > > B(2,4) = Q*C'+M'*D12';
> > > B(2,5) = M';
> > > B(2,6) = Q;
> > > B(3,3) = -gammar^2*eye(size(B1,2));
> > > B(3,4) = D11';
> > > B(4,4) = -eye(size(Cd,1))+Cd*S1*Cd'+Dd*S2*Dd';
> > > B(5,5) = -S2;
> > > B(6,6) = -S1;
> > >
> > > % set up all constraints
> > > Constraints = [B < 0, Q>0, S1>0, S2>0];
> > > solvesdp(Constraints)
> > > yalmiptime: 0.3430
> > > solvertime: 1.3440
> > > info: 'No problems detected (SeDuMi-1.1)'
> > > problem: 0
> > > dimacs: [1.4589e-015 0 0 0 7.3848e-016
3.9007e-
> > 015]
> > >
> > >
> > > >> double(Q)
> > >
> > > ans =
> > >
> > > 0.2425 -0.2091
> > > -0.2091 1.0081
> > >
> > > >> double(S1)
> > >
> > > ans =
> > >
> > > 1.3613 -0.4978
> > > -0.4978 2.3019
> > >
> > > >> double(S2)
> > >
> > > ans =
> > >
> > > 2.0517
> > >
> > > >> double(M)
> > >
> > > ans =
> > >
> > > -0.1367 -0.6933
> > >
> > >
> > >
> > This LMI example is what I read from a paper, but the
> > author's result is different form yours. And he gave
> > proofs, I think the author only use matlab and we use
other
> > toolboxes. I doubt if there really exists result
difference
> > because of toolboxes?
> >
> > The paper's address is
http://www.sciencedirect.com/science?
> > _ob=ArticleURL&_udi=B6V21-3WWV8W6-
B&_user=10&_coverDate=08%
> > 2F31%
> >
2F1999&_alid=736573613&_rdoc=1&_fmt=high&_orig=search&_cdi=5
> >
689&_sort=d&_docanchor=&view=c&_ct=1&_acct=C000050221&_versi
> >
on=1&_urlVersion=0&_userid=10&md5=8ecef13fb66b50ddc4a3990637
> > 4c61b7
>
>
> The solution is not unique since you only solve a
> feasibility problem
>
>
Thank you very much. According to this, I have a lot to
learn.