A graph theoretic approach to input-to-state stability of switched systems

TL;DR

This paper introduces a graph-theoretic method to analyze input-to-state stability of discrete-time switched systems, allowing for non-ISS subsystems and providing a class of stabilizing switching signals with simple construction.

Contribution

It develops a novel graph-based framework to characterize ISS of switched systems, including non-ISS components, and offers an algorithmic way to generate stabilizing switching signals.

Findings

A weighted digraph models the switched system dynamics.

A class of periodic switching signals ensures ISS.

The method accommodates non-ISS subsystems in the analysis.

Abstract

This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of nonlinear systems with exogenous inputs, we present a class of switching signals under which the resulting switched system is ISS. We allow non-ISS systems in the family and our analysis involves graph-theoretic arguments. A weighted digraph is associated to the switched system, and a switching signal is expressed as an infinite walk on this digraph, both in a natural way. Our class of stabilizing switching signals (infinite walks) is periodic in nature and affords simple algorithmic construction.