# Mult&T

### Franklin Pineda (view profile)

Find realizations of multivariable systems. Created for Msc. students at the UANDES and UAC.

[A B C D]=lmpf2ss(D1,N)
```function [A B C D]=lmpf2ss(D1,N)
%LMPF2SS Finds the  realization by method fraction coprime of a LTI
% MIMO SYS model
%
% Syntax:  [A,B,C,D] = lmpf2ss(D,N)
%
% Inputs:
%    SYS - LTI MIMO system, in Matrix Transfer Function
%    representation.
%
% Outputs:
%    A -
%    B -
%    C -
%    D - space-state representation
%
% Example:
%   G1=tf([1 0],conv(conv([1 1],[1 1]),conv([1 2],[1 2])));
%   G2=tf(conv([1 0],conv([1 1],[1 1])),conv(conv([1 1],[1 1]),conv([1 2],[1 2])));
%   G3=tf(-conv([1 0],conv([1 1],[1 1])),conv(conv([1 1],[1 1]),conv([1 2],[1 2])));
%   G4=tf(-conv([1 0],conv([1 1],[1 1])),conv(conv([1 1],[1 1]),conv([1 2],[1 2])));
%   Gt=[G1 G2; G3 G4];
%   [A,B,C,D]=lmpf2ss(Gt)
%
% Other m-files required:
% Subfunctions: v=findv(D)
%                         [Ar]=fcc4(vi,vf,g,i)
%                         G=rmdf2mtf(D1,N);
%                         [Gsp D]=mtfsp(G);
%
% Author: Franklin Pineda Torres
% email: fe.pineda92@uniandes.edu.co
% Created: July 2008;
% Last revision: 31-Dec-2008;

% May be distributed freely for non-commercial use,
% but please leave the above info unchanged, for
% credit and feedback purposes

%------------- BEGIN CODE --------------
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
G=lcf2mtf(D1,N);
[Gsp D]=mtfsp(G);
[D1 N]=mtf2lmpf(Gsp);
v=findv(D1,'cf');
[fd cd1]=size(D1);
k1=1;C=[];
k=eye(length(v));
[fn cn]=size(N);
for i=1:fn,
k2=1;
for m=1:v(i),
for j=1:cn,
while N{i,j}(1)==0
N{i,j}(1)=[];
if length(N{i,j})==1||length(N{i,j})==0
if isempty(N{i,j})
N{i,j}=0;
end
break;
end
end
lf=length(roots(N{i,j}));
if lf>=(m-1)
if m==1
pos=lf+1;
else
pos=lf-(m-2);
end
B(k1,j)=N{i,j}(pos);
else
B(k1,j)=0;
end
end
k1=k1+1;
if k2==v(i),
C=cat(2,C,k(:,i));
else
C=cat(2,C,zeros(fn,1));
end
k2=k2+1;
end
for j1=1:cd1,
g=D1{i,j1};
if j1==i
b=1;
else
b=0;
end
if v(i)==0 || v(j1)==0
continue;
end
Ar{i,j1}=fcc4(v(i),v(j1),g,b);
end
end
A=cell2mat(Ar);

%%%%%%%-----SUBFUNCTION-----%%%%%
function [Ar]=fcc4(vi,vf,g,i)
g=-fliplr(g);
Ar=zeros(vi,vf);
lg=length(g);
for j=1:vi
if j<=lg
Ar(j,vf)=g(j);
else
Ar(j,vf)=0;
end
end
if i==1
if vi==vf
Ar(2:vf,1:(vf-1))=eye(vi-1);
end
end
return
```