LMI solution to Discrete Lyapunov Equation

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)

Answer 1

[SANDEEP SURAVARAPU]

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