Input-to-State Stability of Discrete-Time Delay Systems with Delayed Impulses

Abstract

This paper investigates the input-to-state stability (ISS) of discrete-time delay systems with delayed impulses. By employing Lyapunov functions together with Razumikhin technique, a number of ISS criteria are obtained. It is shown that if the original impulse-free system has no ISS property, it can become input-to-state stable by adding certain impulsive controls which are stabilizing. Correspondingly, the original system without impulses can retain its ISS property with appropriate impulsive perturbations which are destabilizing. Then, robust ISS property for a class of uncertain discrete-time delay systems with delayed impulses is considered. Finally, some numerical examples are given to illustrate the effectiveness and the superiority of the results.