LMI-based Design of Robust Static Output Feedback Controller for Uncertain Linear Continuous Systems

This paper proposes the static output feedback (SOF) controller design method for uncertain linear continuous-time systems based on the Linear Matrix Inequalities (LMIs) technique. In the present work, we consider norm-bounded parametric uncertainties. We show that the existence of the SOF for the closed-loop uncertain linear systems is cast as the feasibility of a set of Bilinear Matrix Inequalities (BMIs). Using some technical lemmas, the BMIs are transformed into LMIs, which are numerically exploitable. Thus, we present new LMI stability conditions for the SOF design using two different approaches. We show that our new LMI conditions are less restrictive compared with those available in the literature. A numerical example is illustrated in the end to show the superiority of our design method.