LMI solution to Discrete Lyapunov Equation

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Discrete Lyapunov Equation inequality is given by
and .
If i consider a feedback to the Linear system then the LMI to be solved is
where and
Now the above system always Outputs Q=[0 0] for any Random A and B matrices and i do not understand why!!!!!!
Could you please help!!!!!!
Note :
Code :
setlmis([]);
P=lmivar(1,[2 1]);
Q=lmivar(2,[1 2]);
lmiterm([1 1 1 P],1,-1); % LMI #1: -P
lmiterm([1 1 1 0],(A1*P+B1*Q)*P^(-1)*(A1*P+B1*Q).');
lmiterm([-2 1 1 P],1,1);
LMItest=getlmis;
[tmin,xfeas] = feasp(LMItest,[0,0,0,0,0],0)
P = dec2mat(LMItest,xfeas,P)
Q = dec2mat(LMItest,xfeas,Q)

Accepted Answer

SANDEEP SURAVARAPU
SANDEEP SURAVARAPU on 8 Jun 2021
I found the mistake....
Posting it so that it would be helpful for others
Solution :
Variable Q is not declared in LMIterm so Matlab doesnt consider it even though it is declared as variable.
So the equation "lmiterm([1 1 1 0],(A1*P+B1*Q)*P^(-1)*(A1*P+B1*Q).')" has to be split to multiple terms

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