Strong ISS implies strong iISS for time-varying impulsive systems

TL;DR

This paper proves that for impulsive systems, strong ISS guarantees strong iISS, extending known results from nonimpulsive and time-varying systems under certain stability assumptions.

Contribution

It demonstrates that strong ISS implies strong iISS for time-varying impulsive systems with enhanced asymptotic stability conditions.

Findings

Strong ISS implies strong iISS for impulsive systems.

The implication holds under stronger asymptotic stability assumptions.

Extends previous results from nonimpulsive and time-varying systems.

Abstract

For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stability (ISS) property is strictly stronger than integral input-to-state stability (iISS). Very recently, we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics, ISS implies iISS also for time-varying systems. In this paper, we show that this implication remains true for impulsive systems, provided that asymptotic stability is understood in a sense stronger than usual for impulsive systems.