Time-delay systems with delayed impulses: A unified criterion on asymptotic stability

TL;DR

This paper presents a unified stability criterion for nonlinear time-delay systems with delayed impulses, applicable to various impulsive systems, and demonstrates its generality through theoretical and numerical analysis.

Contribution

It introduces a comprehensive stability criterion for nonlinear time-delay systems with delayed impulses, covering all combinations of stabilizing and destabilizing dynamics.

Findings

The criterion is more general than existing results.

The method applies to systems with different stabilizing/destabilizing components.

Numerical examples validate the theoretical findings.

Abstract

The paper deals with the global asymptotic stability of general nonlinear time-delay systems with delay-dependent impulses through the Lyapunov-Krasovskii method. We derive a unified stability criterion which can be applied to a variety of impulsive systems. The cases when each of the continuous dynamics and the impulsive component is either stabilizing or destabilizing are investigated. Both theoretically and numerically, we demonstrate that the obtained result is more general than those existing in the literature.