This paper investigates input-to-state stability (ISS) for a class of discrete time-delay systems with switching and impulsive signals. By the Lyapunov–Krasovskii technique, a dwell-time bound and delay bound are clearly presented to contribute to the ISS for discrete time-delay systems. A significant subsequence method of the switched and impulsive sequence will firstly be applied to study the ISS of discrete systems. Based on this method, some new conditions guaranteeing ISS are presented. Compared with the existing results on related problems, the obtained stability criteria are less conservative as it is only required for the specially designed Lyapunov function to be non-increasing along each of the defined subsequences of the switched and impulsive time. Examples of network control systems are presented to illustrate the main results at the end.
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