Construction of time-varying ISS-Lyapunov Functions for Impulsive Systems

TL;DR

This paper introduces a method to construct time-varying ISS-Lyapunov functions for impulsive systems, enhancing stability analysis by providing necessary and sufficient conditions that handle systems with complex dynamics.

Contribution

It presents a novel approach to derive time-varying ISS-Lyapunov functions from candidate functions, bridging the gap between ease of construction and guaranteed stability conditions.

Findings

Provides a constructive method linking candidate and time-varying ISS-Lyapunov functions.

Enables stability analysis of impulsive systems with simultaneous instability.

Enhances the tools available for ISS stability verification.

Abstract

Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition. Moreover, time-varying ISS-Lyapunov functions cover systems with simultaneous instability in continuous and discrete dynamics for which candidate ISS-Lyapunov functions remain inconclusive. The present paper links these two concepts by suggesting a method of constructing time-varying ISS-Lyapunov functions from candidate ISS-Lyapunov functions, thereby effectively combining the ease of construction of candidate ISS-Lyapunov functions with the guaranteed existence of time-varying ISS-Lyapunov functions.