New stability conditions for discrete-time switched systems with time-varying delay under arbitrary switching signal and with average dwell time approach

This paper discusses the problems of stability analysis for a class of discrete-time switched systems with time-varying delay in which both arbitrary switching signal and Average Dwell Time (ADT) switching are considered. New sufficient conditions guaranteeing the exponential stability of the studied system are proposed and developed by constructing an appropriate multiple Lyapunov-Krasovskii functional, via an arbitrary switching law firstly and with average dwell time switching in the other hand. Furthermore, the discrete Wirtinger-based inequality approach is employed with an improved Reciprocally Convex Lemma in order to develop our method and to improve less conservative results over than some recent works. The obtained conditions are established in a form of a set of strict linear matrix inequalities (LMIs). Finally, numerical examples are given to illustrate and to demonstrate the effectiveness of the proposed method and to compare the obtained results with some previous works in the literature.