Input/output‐to‐state stability of nonlinear impulsive delay systems based on a new impulsive inequality

In this paper, input/output‐to‐state stability (IOSS) and integral IOSS (iIOSS) are investigated for nonlinear impulsive systems with delay. Based on a new impulsive inequality, we propose some sufficient criteria for IOSS and iIOSS of impulsive delay systems. It is shown that the obtained results for IOSS and iIOSS are regardless of the length of the impulsive interval and the size of time delay if the impulsive gain satisfies a given condition. In addition, based on the average impulsive interval method, some more useful sufficient conditions are derived for IOSS and iIOSS of impulsive delay systems with persistent large‐scale destabilizing impulses. Furthermore, a relationship is established among the average impulsive interval, impulses, time delay, and the decay of the system without impulses such that the impulsive delay system is input/output‐to‐state stable and integral input/output‐to‐state stable, respectively. Two examples are given to show the validity of the obtained results.

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