Input-to-state stability for impulsive switched systems with delays based on a class of generalised impulsive and switching signals

The input-to-state stability (ISS) for discrete-time impulsive switched systems with delays is investigated, which contains both stable and unstable subsystems. By utilising the multiple Lyapunov-Krasovskii functionals (MLKFs), the delay effects, which are divided into delay-independent part and delay-dependent part, have been processed. Some sufficient conditions are presented to ensure the ISS of system, provided that the switchings and the impulses do not occur too frequently and the activation time of unstable subsystems is comparatively short. Meanwhile, a relationship is built up among admissible edge-dependent average dwell time (AED-ADT), admissible edge-dependent average impulsive interval (AED-AII), impulses magnitude, and decaying/increasing rates of the Lyapunov function. Contrast to previous works, some improvements are made: the effect of delays are fully explored, and the resulting ISS criteria are available with different impulses; AED-AII is first proposed , and combined with AED-ADT to handle the stability problem. Two numerical examples are given to illustrate the theoretical results.