Input-to-State Stability of Nonlinear Impulsive Systems with Hybrid Impulses

This note investigates input-to-state stability (ISS) of nonlinear impulsive systems with hybrid impulses. Such systems contain a time-dependent jump map that can generate both stabilizing and destabilizing impulsive jumps. To cope with the two-fold effect of impulses within a single impulse time sequence, we use the concept of average impulsive gain. We provide novel sufficient conditions for ISS in terms of exponential ISS-Lyapunov function equipped with average impulsive gain and appropriate dwell-time condition. Contrary to the existing results we do not impose severe restrictions on impulsive gains, like periodicity or a finite number of different gains. Finally, we demonstrate effectiveness of our results by concluding ISS for a system whose ISS property cannot be verified by any other result available in the literature. Copyright (c) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)