Stability criteria for singularly perturbed impulsive linear switched systems

TL;DR

This paper develops stability criteria for impulsive linear switched systems with singular perturbations by analyzing auxiliary systems, enabling the determination of stability or instability of the original system in the small perturbation regime.

Contribution

It introduces a novel approach using auxiliary systems to assess stability of singularly perturbed impulsive switched systems, bridging the analysis between different time scales.

Findings

Auxiliary systems effectively predict stability of original systems.

Stability depends on the behavior of auxiliary systems in the small perturbation limit.

Method provides a practical tool for stability analysis in complex switched systems.

Abstract

We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove that the stability or instability of these auxiliary systems directly determines that of the original system in the regime of small singular perturbation parameters.