Stability Analysis of Continuous-Time Switched Systems with a Random Switching Signal

TL;DR

This paper investigates the stochastic stability of continuous-time switched systems with a hybrid dwell time, providing necessary and sufficient conditions via linear matrix inequalities, and illustrates the impact of randomness through numerical examples.

Contribution

It introduces a novel stability analysis framework for systems with mixed fixed and random dwell times using Lyapunov methods and linear matrix inequalities.

Findings

Stability conditions are characterized by linear matrix inequalities.

Random dwell times influence system stability as demonstrated by numerical examples.

The approach provides a comprehensive understanding of stochastic effects on switched systems.

Abstract

This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part. The stochastic stability of such switched systems is studied using a Lyapunov approach. A necessary and sufficient condition is established in terms of linear matrix inequalities. The effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition.