Generalized switching signals for input-to-state stability of switched systems

TL;DR

This paper introduces a new class of switching signals that ensure input-to-state stability in switched nonlinear systems, even when not all systems are ISS, surpassing traditional average dwell time methods.

Contribution

It characterizes a novel, more general class of switching signals that guarantee ISS, expanding beyond average dwell time constraints in switched system stability analysis.

Findings

New class of switching signals guarantees ISS

Allows faster switching than average dwell time

Recasts and extends prior stability results

Abstract

This article deals with input-to-state stability (ISS) of continuous-time switched nonlinear systems. Given a family of systems with exogenous inputs such that not all systems in the family are ISS, we characterize a new and general class of switching signals under which the resulting switched system is ISS. Our stabilizing switching signals allow the number of switches to grow faster than an affine function of the length of a time interval, unlike in the case of average dwell time switching. We also recast a subclass of average dwell time switching signals in our setting and establish analogs of two representative prior results.