Exponential stability and stabilization for uncertain discrete-time periodic systems with time-varying delay

Abstract

This article addresses the problems of robustly exponential stability and exponential stabilization for uncertain linear discrete-time periodic systems with time delay in the state variables and polytopic-type parameter uncertainty. By constructing the novel uncertainty-dependent Lyapunov–Krasovskii functionals, we establish some sufficient conditions in forms of linear matrix inequalities, which guarantee the uncertain linear discrete-time periodic system with time delay is robustly exponentially stable. Then, by utilizing static periodic state feedback and free weighting matrix technique, we give some sufficient conditions to ensure the robustly exponential stabilization of uncertain linear discrete-time periodic systems with time delay. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.