Almost Sure Stability and Stabilization of Markovian Jump Systems With Stochastic Switching

Abstract

This article addresses the exponential almost sure (EAS) stability and stabilization problems of continuous-time Markovian jump systems with additional stochastic switches. Sufficient conditions for EAS stability are established by applying a method to its stochastic transfer matrix. Particularly, both sojourn time and distribution of such random switchings are considered in the design of a state-feedback controller. Compared with some existing references, the proposed controller could bear unmatched or asynchronous signals. Moreover, it can be seen that our results are more general but less conservative, when the information on sojourn time and distribution is used. Some of them include previous work as special cases. Two examples are used to demonstrate the effectiveness and superiority of the methods proposed in our study.