Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov–Krasovskii functional

This paper is concerned with the stability and stabilization problems for discrete-time systems with interval time-varying delays. By construction of an augmented Lyapunov–Krasovskii functional and utilization of zero equalities, improved delay-dependent criteria for asymptotic stability of the systems are derived in terms of linear matrix inequalities (LMIs). Based on the proposed stability criteria, a sufficient condition for designing feedback gains of time-delayed controllers which guarantee the stability of the concerned system is presented. Through three numerical examples, the effectiveness to enhance the feasible region of the proposed criteria is demonstrated.