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Thread Subject:
kronecker product in LMIs

Subject: kronecker product in LMIs

From: Luis Félix

Date: 27 Dec, 2008 00:19:02

Message: 1 of 4

I am using tMATLAB?s lmi editor. I am having problems with

[kron(L,P)+kron(M,A*P)]<0

The errors are:
1. Constant terms in diagonal blocks must be symmetric
2. Error using + dimension must agree.

Matrices L, P, M and A are of proper dimension, I verified twice.
L, M and A are constant matrices and P is a variable matrix. It is a Lyapunov symmetric matrix, propery defined.
I have another LMIs and everything worked fine until I added the kronecker product.

I hope someone can help me with this issue. I am reading the .pdf LMI toolbox guide but I have not found anything regarding the use of kronecker product in MATLAB lmi editor.

Luis Carlos

Subject: kronecker product in LMIs

From: Roger Stafford

Date: 27 Dec, 2008 01:53:03

Message: 2 of 4

"Luis Felix" <luisc_felix@hotmail.com> wrote in message <gj3s9m$mvv$1@fred.mathworks.com>...
> I am using tMATLAB?s lmi editor. I am having problems with
>
> [kron(L,P)+kron(M,A*P)]<0
>
> The errors are:
> 1. Constant terms in diagonal blocks must be symmetric
> 2. Error using + dimension must agree.
> ......

  That second error sounds as if the sizes of your matrices are actually incorrect. You have to satisfy three requirements here: 1) the number of columns in L is the same as the number of columns in M (for valid addition,) 2) the product of the number of rows in L and in P must equal the product of the number of rows in M and in A, (also for valid addition,) and 3) the number of columns in A must equal the number of rows in P (for a valid matrix product.)

Roger Stafford

Subject: kronecker product in LMIs

From: Luis Félix

Date: 28 Dec, 2008 01:13:02

Message: 3 of 4

Mr. Stafford,

Sorry to bother you again, I`ll extend my case because last time I did not include enough information.

I enter the following matrices:

A1=[0 1;17.29 0];
A2=[0 1;10.576 0];
B1=[0;-0.176];
B2=[0;-0.026];
Cz=[0.01 0;0 0];
D=[0;0.01];
Bw=[0;0.01];
L=[-9.9 -10;-10 -9.9];
M=[0 1;0 0];

I open the lmi editor and define the following variables

setlmis([]);
P=lmivar(1,[2 1]);
Y1=lmivar(2,[1 2]);
Y2=lmivar(2,[1 2]);

The Pmatrix is the Lyapunov matrix, positive definite

I enter the following lmis:

[A1*P+P*A1'+B1*Y1+Y1'*B1' Bw P*Cz'+Y1'*D'; Bw' -0.01 0;Cz*P+D*Y1 0 -1]<0 %LMI1

[A1*P+P*A1'+B1*Y2+Y2'*B1' Bw P*Cz'+Y2'*D'; Bw' -0.01 0;Cz*P+D*Y2 0 -1]<0 %LMI2

[A2*P+P*A2'+B2*Y1+Y1'*B2' Bw P*Cz'+Y1'*D'; Bw' -0.01 0;Cz*P+D*Y1 0 -1]<0 %LIM3

[A2*P+P*A2'+B2*Y2+Y2'*B2' Bw P*Cz'+Y2'*D'; Bw' -0.01 0;Cz*P+D*Y2 0 -1]<0 %LMI4

[kron(L,P)+kron(M,A1*P)+kron(M,B1*Y1)]<0 %LMI5

P>0

All matrices have correct dimensions and comply with kronecker product, matrix multiplication and matrix addition. The first 4 LMI do have any problem, (I already run those), but when I add the fifth lmi, a problem arises.

??? Error using ==> plus
Matrix dimensions must agree

I double checked the matrices dimensions, they all agree. IN the kronecker product, the first term kron(L,P) generates a 4X4 matrix, as well as th second and third terms.

It is possible that I am using a wrong command for the kronecker product?

In adittion, in LMI5, If I keep only the term kron(M,A1*P), when I load the lms descriptions, I get this error message:

??? Error using ==> lmiterm
LMI #5, block (1,1): constant terms in diagonal blocks must be symmetric

Do you now about these error messages?

Thank you,

Luis Carlos Felix



"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <gj41pu$724$1@fred.mathworks.com>...
> "Luis Felix" <luisc_felix@hotmail.com> wrote in message <gj3s9m$mvv$1@fred.mathworks.com>...
> > I am using tMATLAB?s lmi editor. I am having problems with
> >
> > [kron(L,P)+kron(M,A*P)]<0
> >
> > The errors are:
> > 1. Constant terms in diagonal blocks must be symmetric
> > 2. Error using + dimension must agree.
> > ......
>
> That second error sounds as if the sizes of your matrices are actually incorrect. You have to satisfy three requirements here: 1) the number of columns in L is the same as the number of columns in M (for valid addition,) 2) the product of the number of rows in L and in P must equal the product of the number of rows in M and in A, (also for valid addition,) and 3) the number of columns in A must equal the number of rows in P (for a valid matrix product.)
>
> Roger Stafford

Subject: kronecker product in LMIs

From: Jose Luis Azcue Puma

Date: 19 Aug, 2009 16:18:03

Message: 4 of 4

Hello Luis

I have the similar problem,how did you resolve your problem?
how did you do?

best regards.

"Luis Felix" <luisc_felix@hotmail.com> wrote in message <gj3s9m$mvv$1@fred.mathworks.com>...
> I am using tMATLAB?s lmi editor. I am having problems with
>
> [kron(L,P)+kron(M,A*P)]<0
>
> The errors are:
> 1. Constant terms in diagonal blocks must be symmetric
> 2. Error using + dimension must agree.
>
> Matrices L, P, M and A are of proper dimension, I verified twice.
> L, M and A are constant matrices and P is a variable matrix. It is a Lyapunov symmetric matrix, propery defined.
> I have another LMIs and everything worked fine until I added the kronecker product.
>
> I hope someone can help me with this issue. I am reading the .pdf LMI toolbox guide but I have not found anything regarding the use of kronecker product in MATLAB lmi editor.
>
> Luis Carlos

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