Input-to-state Stability of Impulsive Systems with Different Jump Maps

TL;DR

This paper establishes conditions under which impulsive systems with time-dependent jump maps are input-to-state stable, using ISS-Lyapunov functions and a small-gain theorem with dwell-time constraints.

Contribution

It introduces a novel small-gain theorem and dwell-time condition for ISS of impulsive systems with varying jump maps, extending stability analysis techniques.

Findings

Provided sufficient conditions for ISS of impulsive systems with time-dependent jumps.

Developed a small-gain theorem tailored for interconnected impulsive systems.

Validated the stability criteria through theoretical proofs.

Abstract

The paper introduces sufficient conditions for input-to-state stability (ISS) of a class of impulsive systems with jump maps that depend on time. Such systems can naturally represent an interconnection of several impulsive systems with different impulse time sequences. Using a concept of ISS-Lyapunov function for subsystems a small-gain type theorem equipped with a new dwell-time condition to verify ISS of an interconnection has been proven.