H∞ control of switched delayed systems with average dwell time

Abstract

This paper considers the problems of stability analysis and H∞ controller design of time-delay switched systems with average dwell time. In order to obtain less conservative results than what is seen in the literature, a tighter bound for the state delay term is estimated. Based on the scaled small gain theorem and the model transformation method, an improved exponential stability criterion for time-delay switched systems with average dwell time is formulated in the form of convex matrix inequalities. The aim of the proposed approach is to reduce the minimal average dwell time of the systems, which is made possible by a new Lyapunov–Krasovskii functional combined with the scaled small gain theorem. It is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature. Moreover, the exponential H∞ controller can be constructed by solving a set of conditions, which is developed on the basis of the exponential stability criterion. Simulation examples illustrate the effectiveness of the proposed method.