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LMI中有关于克罗内克积的决策变量，如何定义？

要求该LMIx小于零的解，其中，A为3x3, IN为5x5单位矩阵，B=[1,0,0]'，S,T,K为决策变量矩阵, S,T均为15x15阶正定对称矩阵, K=[x, y, z]的1x3阶阵。

我编出的错误，都不知道为何出这样的错。

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

运行错误：

Error using lmiterm (line 309)

lhs of LMI #4, block (2,1): term dimensions incompatible with

other terms in same column

Error in LMI_SMAS (line 108)

lmiterm([bamlmi4 1 2 M],1,1);

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

以下是代码

global A B H K IN In S T A_tilde B_tilde D L mu

% format long

format

N=5;         % 节点个数

n=3;         % 维数

IN=eye(N);

In=eye(n);

A=[ -0.40 -0.20  0.020;

-0.2  0.1  0.21;

-0.04 -0.76 -0.11];

B=[1 0 0]';

K=[1.71  -7.43 -0.79];

A_tilde=[ 0 1 0 0 1;        % 邻接矩阵

0 0 1 0 1;

1 0 0 1 0;

0 0 1 0 1;

1 0 0 1 0];

B_tilde=diag([1 1 0 0 0]);  % 牵引矩阵

% 求拉氏矩阵

d=zeros(N,1);

for i=1:N

d(i)=sum(A_tilde(i,:));

end

D=diag([d(1),d(2),d(3),d(4),d(5)]);

L=D-A_tilde;      % 拉氏矩阵

H = L + B_tilde;

A1=kron(IN,A);

I2=kron(IN,In);

%  mu=1;

%  sP=B*K;

s=N*n;

% sM=kron(H,sP);

% sR=kron(IN,sP);

for alfa=0:0.1:10

%初始化LMI系统

setlmis([]);

%定义决策变量

S=lmivar(1,[s 1]);

T=lmivar(1,[s 1]);

mu=lmivar(1,[1 1]);

[P,n,sP]=lmivar(2,[n n]);

%         [M,n,sM]=lmivar(3,[H(1,1)*sP, H(1,2)*sP, H(1,3)*sP, H(1,4)*sP, H(1,5)*sP; ...

%                            H(2,1)*sP, H(2,2)*sP, H(2,3)*sP, H(2,4)*sP, H(2,5)*sP; ...

%                            H(3,1)*sP, H(3,2)*sP, H(3,3)*sP, H(3,4)*sP, H(3,5)*sP; ...

%                            H(4,1)*sP, H(4,2)*sP, H(4,3)*sP, H(4,4)*sP, H(4,5)*sP; ...

%                            H(5,1)*sP, H(5,2)*sP, H(5,3)*sP, H(5,4)*sP, H(5,5)*sP]);

%         [R,n,sR]=lmivar(3,[IN(1,1)*sP, IN(1,2)*sP, IN(1,3)*sP, IN(1,4)*sP, IN(1,5)*sP; ...

%                            IN(2,1)*sP, IN(2,2)*sP, IN(2,3)*sP, IN(2,4)*sP, IN(2,5)*sP; ...

%                            IN(3,1)*sP, IN(3,2)*sP, IN(3,3)*sP, IN(3,4)*sP, IN(3,5)*sP; ...

%                            IN(4,1)*sP, IN(4,2)*sP, IN(4,3)*sP, IN(4,4)*sP, IN(4,5)*sP; ...

%                            IN(5,1)*sP, IN(5,2)*sP, IN(5,3)*sP, IN(5,4)*sP, IN(5,5)*sP]);

[M,n,sM]=lmivar(3,[H(1,1)*P, H(1,2)*P, H(1,3)*P, H(1,4)*P, H(1,5)*P; ...

H(2,1)*P, H(2,2)*P, H(2,3)*P, H(2,4)*P, H(2,5)*P; ...

H(3,1)*P, H(3,2)*P, H(3,3)*P, H(3,4)*P, H(3,5)*P; ...

H(4,1)*P, H(4,2)*P, H(4,3)*P, H(4,4)*P, H(4,5)*P; ...

H(5,1)*P, H(5,2)*P, H(5,3)*P, H(5,4)*P, H(5,5)*P]);

[R,n,sR]=lmivar(3,[IN(1,1)*P, IN(1,2)*P, IN(1,3)*P, IN(1,4)*P, IN(1,5)*P; ...

IN(2,1)*P, IN(2,2)*P, IN(2,3)*P, IN(2,4)*P, IN(2,5)*P; ...

IN(3,1)*P, IN(3,2)*P, IN(3,3)*P, IN(3,4)*P, IN(3,5)*P; ...

IN(4,1)*P, IN(4,2)*P, IN(4,3)*P, IN(4,4)*P, IN(4,5)*P; ...

IN(5,1)*P, IN(5,2)*P, IN(5,3)*P, IN(5,4)*P, IN(5,5)*P]);

bamlmi1=newlmi;

lmiterm([-bamlmi1 1 1 S],1,1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

bamlmi2=newlmi;

lmiterm([-bamlmi2 1 1 T],1,1);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

bamlmi3=newlmi;

lmiterm([-bamlmi3 1 1 mu],1,1);

%%%%%

bamlmi4=newlmi;

lmiterm([bamlmi4 1 1 0],A1+A1');

lmiterm([bamlmi4 1 1 mu],I2,1);

%         lmiterm([bamlmi4 1 1 0],mu*I2);

lmiterm([bamlmi4 1 2 M],1,1);

lmiterm([bamlmi4 1 2 -M],1,1);

lmiterm([bamlmi4 1 3 R],1,1);

lmiterm([bamlmi4 1 3 -R],1,1);

%         lmiterm([bamlmi4 1 2 0],sM);

%         lmiterm([bamlmi4 1 2 0],sM');

%

%         lmiterm([bamlmi4 1 3 0],sR');

%         lmiterm([bamlmi4 1 3 0],sR);

lmiterm([bamlmi4 2 3 0],0*I2);

lmiterm([bamlmi4 2 2 S],-1,1);

lmiterm([bamlmi4 3 3 T],-1,1);

%         lmiterm([bamlmi4 1 3 (kron(IN,B*K))'+kron(IN,B*K)],1,1);

lmiterm([bamlmi4 1 1 0],alfa*I2);

%         lmiterm([bamlmi4 2 2 0],alfa*I2);

%         lmiterm([bamlmi4 3 3 0],alfa*I2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

lcdlmis=getlmis;

[tmin,xfeas]=feasp(lcdlmis);

if tmin<0

S=dec2mat(lcdlmis,xfeas,S);

T=dec2mat(lcdlmis ,xfeas,T);

M=dec2mat(lcdlmis ,xfeas,M);

R=dec2mat(lcdlmis ,xfeas,R);

mu=dec2mat(lcdlmis ,xfeas,mu);

O=A1+A1'+mu*I2+(sM'+sM)'*inv(S)*(sM'+sM)+(sR+sR')'*inv(T)*(sR'+sR);

OO=[A1+A1'+mu*I2, (sM'+sM)',  (sR+sR')';

(sM'+sM), -S, zeros(15);

(sR+sR'), zeros(15),-T];

%             if -alfa + max(eig(S))+ max(eig(T)) < 0

disp('******************************* Here is a feasible solution ********************************');

alfa

%             K=dec2mat(lcdlmis,xfeas,K)

%             P=dec2mat(lcdlmis,xfeas,P)

%             min(eig(O)) + max(eig(S))+ max(eig(T)) < 0

S

T

mu

return

%             end

end

end

2246.tmp.png

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2246.tmp.png

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