Problem solving LMI, strange results

[Pedro Vicente]

Hey guys, I'm trying to solve the LMI that is attached. I get a result but it is very far from the right result. Can somebody tell me what is wrong? Is it the LMI badly choose? When I put the results in the simulation my system gets unstable, but when I use the values that it is in the article the system is stable, meaning that there is a right result. The code is attached, I had to choose a value for gamma, because it wouldn't work with gamma as variable.

[Johan Löfberg]

You want X>=0

Note that strict inequalities are not supported (YALMIP screams at you about this), and the flag 'symmetric' is redundant as the matrices are square anyway

[Pedro Vicente]

So, I just need to add a constraint X>=0 and it will work? Also, there is a way to implement a strict inequality?

[Johan Löfberg]

Yes

A strict semidefinite constrint would be X >= margin*eye(n) where margin is your definition of positive definite enough, which still makes sense in a numerical sense, a solvers only work with a precision of, say, 1e-8 or so anyway

[Pedro Vicente]

Hey Johan, it worked very well. I don't get the same results of the article, but my results now make the system stable. Thank you so much. You saved me a lot of time.

[Johan Löfberg]

it would be magic if you obtained the same solution as you're only solving a feasibility problem

[Pedro Vicente]

Yeah, you're totally right. Anyway, thank you again