Asymptotic stability in probability of singular stochastic systems with Markovian switchings

Abstract

Summary This paper investigates the problem of asymptotic stability in probability for singular stochastic systems with Markovian switchings. A stochastic Lyapunov theorem on asymptotic stability in probability for the considered systems is provided. Also, we show that the original system has the same stability property as its difference‐algebraic form based on singular value decomposition. By utilizing the earlier results, a sufficient condition is obtained in terms of linear matrix inequalities, which is easy to check by using standard software. Copyright © 2017 John Wiley & Sons, Ltd.