Stabilizing Graph-dependent Switched Systems

TL;DR

This paper establishes stability conditions for graph-dependent switched systems, including those with non-Hurwitz subsystems, and introduces a slow-fast switching mechanism to ensure overall stability.

Contribution

It provides new sufficient stability conditions for continuous-time linear switched systems governed by graphs, accommodating non-Hurwitz subsystems and a novel slow-fast switching strategy.

Findings

Derived stability conditions for graph-dependent switched systems.

Applicable to systems with non-Hurwitz subsystems.

Introduced a slow-fast switching mechanism for stability.

Abstract

We give sufficient conditions for stability of a continuous-time linear switched system consisting of finitely many subsystems. The switching between subsystems is governed by an underlying graph. The results are applicable to switched systems having some or all non-Hurwitz subsystems. We also present a slow-fast switching mechanism on subsystems comprising simple loops of underlying graph to ensure stability of the switched system.