Asymptotic characterization of destabilizing switching signals for switched linear systems

Abstract

This paper deals with destabilizing switching signals for continuous-time switched linear systems. Our contributions are twofold: Firstly, we propose a class of switching signals under which a switched system is unstable. Our characterization of instability depends solely on the asymptotic behaviour of frequency of switching, frequency of transition between subsystems, and fraction of activation of subsystems. Secondly, we show that our class of destabilizing switching signals is a strict subset of the class of switching signals that does not satisfy asymptotic characterization of stability recently proposed in the literature. This observation identifies a gap between asymptotic characterizations of stabilizing and destabilizing switching signals for switched linear systems.