Switched Output Feedback Stabilization of Discrete-Time Switched Systems

Abstract

This paper addresses the problem of switched static output feedback control for a particular class of discrete-time switched systems under arbitrary switching sequences. The considered class of systems is characterized by a particular structure of the control matrices. Our main contribution consists in new sufficient linear matrix inequality (LMI) conditions for the synthesis of a switched controller. The proposed solution uses congruence transformations and is based on the existence of a switched quadratic Lyapunov function that guarantees the asymptotic stability of the closed-loop system. In addition to the numerical tractability of the LMIs, the main advantage of our new conditions resides in the fact that they work successfully for systems for which the existing conditions fail. Our claim is supported by numerical examples that we present in the paper