Asymptotic stability and stabilization of discrete-time switched systems with time-varying delay

This article deals with the problems of stability and stabilization for a class of discrete-time switched systems with time-varying delay under arbitrary switching signal. First, sufficient conditions guaranteeing the asymptotic stability of the unforced system are developed, by using the switched Lyapunov-Krasovskii functional method. Then, based on the obtained results, a state feedback controller is designed in order to ensure the asymptotic stability of the closed-loop system. Furthermore, slack variables are introduced for more relaxation. The proposed approach is proved to have some less conservative results than some existing works. Finally, numerical examples are provided to illustrate the effectiveness and the merit of the proposed method and to compare the obtained results with some previous works in the literature.