Stabilizing switching signals for switched linear systems

TL;DR

This paper introduces a new class of switching signals that ensure the global asymptotic stability of continuous-time switched linear systems, even with unstable dynamics, by analyzing switching frequency, activation fractions, and transition densities.

Contribution

It characterizes stabilizing switching signals using asymptotic properties and extends previous results with novel techniques involving multiple Lyapunov-like functions.

Findings

Identifies conditions for stability under constrained switching.

Extends stability analysis to systems with unstable dynamics.

Employs multiple Lyapunov-like functions for characterization.

Abstract

This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which the switched linear system generated by it and the family of systems is globally asymptotically stable. Our characterization of such stabilizing switching signals involves the asymptotic frequency of switching, the asymptotic fraction of activation of the constituent systems, and the asymptotic densities of admissible transitions among them. Our techniques employ multiple Lyapunov-like functions, and extend preceding results both in scope and applicability.