Improved Stability Criteria for Discrete-Time Switched Systems With Time-Varying Delay Using Relaxed Summation Inequality

This paper deals with the stability analysis of discrete-time switched systems with time-varying delay governed by an arbitrary switching law. By constructing a multiple Lyapunov-Krasovskii functional and employing a relaxed summation inequality, new sufficient criteria are established and validated to guarantee the asymptotic stability of the studied system. The proposed criteria rely on both the lower and upper bounds of the delay and are formulated as Linear Matrix Inequalities (LMIs). Moreover, additional slack variables are incorporated to provide more relaxation in the analysis of the system under consideration. As a result, the proposed method is demonstrated to produce less conservative results compared to recent studies in the literature. Some numerical examples are performed to show the advantage and effectiveness of the proposed approach.