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.

Keywords:

• Switching signals
• Poisson processes
• Markov processes
• stability analysis
• joint spectral radius

Acknowledgments

The author would like to thank the anonymous reviewers for their detailed comments that helped in improving the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The author's research was supported by the National Natural Science Foundation of China under Grant 61573131.