New results on stability analysis and stabilization of time-delay continuous Markovian jump systems with partially known rates matrix

Abstract

Summary In this note, the problems of stability analysis and controller synthesis of Markovian jump systems with time-varying delay and partially known transition rates are investigated via an input–output approach. First, the system under consideration is transformed into an interconnected system, and new results on stochastic scaled small-gain condition for stochastic interconnected systems are established, which are crucial for the problems considered in this paper. Based on the system transformation and the stochastic scaled small-gain theorem, stochastic stability of the original system is examined via the stochastic version of the bounded realness of the transformed forward system. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a precise approximation of the time-varying delay and the new result on the stochastic scaled small-gain theorem. The proposed stability condition is demonstrated to be much less conservative than most existing results. Moreover, the problem of stabilization is further solved with an admissible controller designed via convex optimizations, whose effectiveness is also illustrated via numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.