Stochastic stability of semi-Markov jump linear systems with uncertain transition rates

Abstract

This paper deals with the robust stochastic stability problem for a class of continuous-time semi-Markov jump linear systems. The system under consideration involves uncertainties both in the transition probabilities and in the system matrices. This new uncertain model generally removes limitations of the certain and time-constant transition rates of jump processes, thus it is appropriate for many practical applications. The sufficient robust stochastic stability criterion for such a class of systems is derived based on multiple Lyapunov function approach. The whole analysis procedure is accomplished by solving a set of linear matrix inequalities. Simulation results illustrate the effectiveness of the proposed method.