ill-condition controller design problems

[Keivan Zavari]

Hi everyone,

Does anyone know why the optimization problems formed by Hinf LMIs are usually ill-conditioned?

I am looking for an analysis or something I can refer to.

Is this the case with other performance criteria? For instance, does H2 also behave similarly?

And final question: How do you prevent or handle this issue?

Thank you.

Regards

Keivan

[Johan Löfberg]

The underlying problem is afaik that the optimal solution pushes an eigenvalue of the closed loop to -inf. This means some decision variables have to grow very large and small. My solution is typically to regularize the objective with terms from these things, or to try to get a feeling for what the optimal objective is, and then solve a feasibility problem where i search for a, say, 5 percent suboptimal solution

[Johan Löfberg]

Employing Kronecker Canonical Form for LMI-Based Synthesis Problems by Anders Helmersson is a nice read on the topic

[Keivan Zavari]

Thank you!