Asymptotic stability conditions for linear coupled impulsive systems with time-invariant subsystems

TL;DR

This paper develops new asymptotic stability conditions for linear coupled impulsive systems with time-invariant subsystems, using Lyapunov functions and discretization methods, applicable even when Floquet theory cannot be used.

Contribution

It introduces a novel approach to analyze stability without assuming subsystem stability, combining Lyapunov and discretization techniques for impulsive systems.

Findings

New stability conditions derived for impulsive systems

Applicable to cases where Floquet theory is not suitable

Illustrated with practical examples

Abstract

This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems, the asymptotic stability property of independent subsystems is not assumed. To analyze the asymptotic stability of a coupled system, the direct Lyapunov method is used in combination with the discretization method. The periodic case and the case when the Floquet theory is not applicable are considered separately. The main results are illustrated with examples.