Input‐to‐state stability of non‐linear impulsive and switched delay systems

Abstract

This study addresses the input-to-state stability (ISS) of non-linear impulsive and switched delay systems. Based on the piecewise Lyapunov-Krasovskii functional method, the authors show that when only some of the constituent subsystems are ISS, the ISS property still can be retained for the non-linear impulsive and switched delay system, if the dwell time of the ISS subsystems satisfies a lower bound condition and the activation time of the non-ISS subsystems satisfies an upper bound condition, respectively. In common parlance, some of the intervals must be overly long, whereas the others must be short enough between impulses. Compared with existing results on related problems, the theory can be applied to a larger class of systems. The proposed approach also enables us to give the analysis of systems involving actuator failure, controller failure or temporary uncertain switching signal. As an example, the authors employ the method to analyse the problem of reliable control for a mechanical rotational cutting process.