Generalized stabilizing controllers for fuzzy systems via Circle criterion — LMI and SOS

We investigate a generalized control problem via the Circle criterion borrowed from system theory; the generalized controller can be cast into existing canonical controllers depending on parameterizations. We first show a fuzzy version of the Circle criterion and then provide a synthesis result based on the Circle criterion, establishing closed-loop stabilizability for state-feedback controllers. In this paper, we show how to incorporating the membership information by approximating the cone of copositive matrices via SOS that is solvable by SOSTOOLS. Finally the validity and applicability of the approach are illuminated by examples.