A probabilistic framework for describing a class of switching signals in continuous-time

Abstract

We present an interpretation of switching signals with certain average dwell time in terms of Poisson process, which allows to build a probabilistic framework to accommodate all the switching signals of this kind. As a result, we can learn more knowledge about such signals. In particular, such a switching signal and the solution of the corresponding switching system jointly constitute a Markov process. And the Markov property will facilitate the asymptotic behaviour analysis of the switching dynamics. As a byproduct, we present an upper bound on the joint spectral radius of a family of Hurwitz or anti-Hurwitz matrices, which turns out to be quite sharp as compared with the existing results.