Solving LMI with YALMIP

[elahe mastani]

Hi , 

I have a LMI problem as attached in this question.

I model this in yalmip but I think it isn't correct because the controller transfer function is not stable.

Thank you for your helping,

Elahe.

[Johan Löfberg]

I strongly doubt that X and Y should be fully parameterized. It looks like a Lyapunov certificates, so they should be be symmetric. As it is now M1<0 is a bunch of elementwise constraitns, while I think you want to have an LMI

https://yalmip.github.io/tutorial/basics/

M3 makes no sense. The png says trace(Q)-gama2 < 0, so I have no idea why you are converting it to a redundant 2x2 LMI

Strict inequalities are not supported. YALMIP is screaming at you about this.

[elahe mastani]

So if YALMIP doesn't support strict inequality. what is your recommendation to me that how can I solve this LMI problem.

Although I use convex as another way but in convex I have the instability of transfer function. 

[Johan Löfberg]

x>=mysmallnumber*I instead of x>0

I have no idea what your other statement is about. Your error is that you are defining x and y as fully parameterized matrices