%直接按F5就能运行得出反馈增益K1,K2,以及传函的最小奇异值，即系统的稳定指标
A1=[0 1.0000;17.2941 0];
A2=[0 1.0000;12.6305 0];
B11=[0.1;0.1];
B12=[0.1;0.1];
B21=[0;-0.1765];
B22=[0;-0.0779];
C1=[11];
C2=[11];
D11=0;
D12=0;
D21=[0.1;0];
D22=[0.1;0];
%
setlmis([]);
X1=lmivar(1,[2,1]);
V1=lmivar(2,[1,2]);
X2=lmivar(1,[2,1]);
V2=lmivar(2,[1,2]);
r1=lmivar(1,[1,1]); %beta_1
%%%%%%
lmiterm([1 1 1 X1],A1,1,'s');
lmiterm([1 1 1 V1],B21,1,'s');
lmiterm([1 1 2 0],B11);
lmiterm([1 3 1 X1],C1,-1);
lmiterm([1 3 1 V1],D21,1);
lmiterm([1 2 2 r1],-1,1);
lmiterm([1 3 2 0],D11);
lmiterm([1 3 3 r1],-1,1);
%
% %%%%%%
lmiterm([2 1 1 X2],A2,1,'s');
lmiterm([2 1 1 V2],B22,1,'s');
lmiterm([2 1 2 0],B12);
lmiterm([2 3 1 X2],C2,-1);
lmiterm([2 3 1 V2],D22,1);
lmiterm([2 2 2 r1],-1,1);
lmiterm([2 3 2 0],D12);
lmiterm([2 3 3 r1],-1,1);
lmiterm([3 1 1 X1],A1,1,'s');
lmiterm([3 1 1 V1],B21,1,'s');
lmiterm([3 1 1 X1],A2,0.5,'s');
lmiterm([3 1 1 V1],B22,0.5,'s');
lmiterm([3 1 1 X2],A1,0.5,'s');
lmiterm([3 1 1 V2],B21,0.5,'s');
lmiterm([3 1 2 0],1.5*B11);
lmiterm([3 1 2 0],0.5*B12);
lmiterm([3 3 1 X1],C1,-1);
lmiterm([3 3 1 V1],D21,1);
lmiterm([3 3 1 X1],C2,-0.5);
lmiterm([3 3 1 V1],D22,0.5);
lmiterm([3 3 1 X2],C1,-0.5);
lmiterm([3 3 1 V2],D21,0.5);
lmiterm([3 2 2 r1],-2,1);
lmiterm([3 3 2 0],1.5*D11);
lmiterm([3 3 2 0],0.5*D12);
lmiterm([3 3 3 r1],-2,1);
lmiterm([4 1 1 X2],A2,1,'s');
lmiterm([4 1 1 V2],B22,1,'s');
lmiterm([4 1 1 X1],A2,0.5,'s');
lmiterm([4 1 1 V1],B22,0.5,'s');
lmiterm([4 1 1 X2],A1,0.5,'s');
lmiterm([4 1 1 V2],B21,0.5,'s');
lmiterm([4 1 2 0],0.5*B11);
lmiterm([4 1 2 0],1.5*B12);
lmiterm([4 3 1 X2],C2,-1);
lmiterm([4 3 1 V2],D22,1);
lmiterm([4 3 1 X1],C2,-0.5);
lmiterm([4 3 1 V1],D22,0.5);
lmiterm([4 3 1 X2],C1,-0.5);
lmiterm([4 3 1 V2],D21,0.5);
lmiterm([4 2 2 r1],-2,1);
lmiterm([4 3 2 0],0.5*D11);
lmiterm([4 3 2 0],1.5*D12);
lmiterm([4 3 3 r1],-2,1);
lmiterm([-95 1 1 X1],1,1);
%
lmiterm([-96 1 1 X2],1,1);
% %%%%
lmiterm([-100 1 1 r1],1,1); %beta_1
%%%%%%%%
lmisys=getlmis;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
n=decnbr(lmisys);
c=zeros(n,1);
for j=1:n
[r1j]=defcx(lmisys,j,r1);
c(j)=trace(r1j);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
options=[1e-6,200,0,0,0]
[tmin,x]=feasp(lmisys,options);
V1=dec2mat(lmisys,x,V1)
V2=dec2mat(lmisys,x,V2)
X1=dec2mat(lmisys,x,X1)
X2=dec2mat(lmisys,x,X2)
K1=V1*(X1^-1)
K2=V2*(X2^-1)
%
r1=dec2mat(lmisys,x,r1) %beta_1
