Stability analysis and controller synthesis of discrete-time switched systems with time delay

This paper studies the problems of stability analysis and H ∞ controller synthesis of switched systems with time-varying delay based on an input–output approach. The attention is focused on developing a new method to further reduce the conservatism of the existing results. The system under consideration is transformed into an interconnection system, and the scaled small gain condition for the interconnection systems is introduced. Based on the system transformation and the scaled small gain theorem, an improved delay-dependent stability criterion is proposed such that the interconnection system is asymptotically stable, which is also proved to guarantee the asymptotic stability of the system based on the direct Lyapunov method in another perspective. The proposed stability condition is demonstrated to be less conservative than most existing results. Moreover, an admissible controller, which solves the problem of H ∞ controller synthesis, is formulated into a convex optimization problem. Illustrative examples are provided to show the advantage and the effectiveness of the proposed method.