New Criteria for Robust Exponential Stability of Uncertain Discrete-Time Switched Systems with Time-Varying Delay via Average Dwell Time Approach and Under Arbitrary Switching Signal

This paper deals with the problems of robust exponential stability for a class of uncertain discrete-time switched systems with time-varying delay and linear fractional perturbations parametric uncertainties, under arbitrary switching signal on the one hand and by using the Average Dwell Time (ADT) approach on the other hand. Firstly, new sufficient conditions guaranteeing the exponential stability of the nominal considered system are proposed and proved, by constructing an augmented Lyapunov–Krasovskii functional, by using the discrete Wirtinger-based inequality combined with an improved form of Reciprocally Convex Lemma (RCL) and by considering the two types of switching signal mentioned above. Then, and based on the obtained results, new criteria are established to ensure the robust exponential stability for uncertain discrete-time switched systems with interval time-varying delay. The established conditions are dependent on the lower and the upper delay bounds and are expressed in terms of Linear Matrix Inequalities (LMIs). Furthermore, some slack variables are introduced by using the Finsler lemma in order to give more relaxation for the studied system. Consequently, the proposed approach is proved to have some less conservative results over than some recent works of the literature. Finally, numerical examples are provided to demonstrate the merit and the effectiveness of the proposed approach.