On the Synthesis of Static Output Feedback Controllers for Guaranteed RMS Gain of Switched Systems with Arbitrary Switching

This paper addresses the problem of determining static output feedback controllers for ensuring desired upper bounds of the root mean square (RMS) gain of continuous-time switched linear systems with arbitrary switching. The problem is addressed by searching for a homogeneous rational Lyapunov function (HRLF) parameterized rationally by the sought controller, and by introducing a polynomial for quantifying the feasibility of the Lyapunov inequalities. It is shown that such a controller exists if and only if a condition built solving three convex optimization problems with linear matrix inequalities (LMIs) holds for polynomials of degree sufficiently large.