A general stability criterion for switched linear systems having stable and unstable subsystems

TL;DR

This paper establishes a general stability criterion for switched linear systems, ensuring asymptotic convergence to zero under certain switching conditions, applicable to various system types including hybrid and mixed stability subsystems.

Contribution

It introduces a unified stability criterion for switched linear systems with stable and unstable subsystems, applicable across continuous, discrete, and hybrid systems.

Findings

Conditions on switching signals guarantee asymptotic stability.

Applicable to systems with stable, unstable, and hybrid subsystems.

Provides a unified framework for stability analysis.

Abstract

We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those having stable subsystems and mixtures of stable and unstable subsystems.