Stochastic stabilizability and passive control for time-delay systems with Markovian jumping parameters

This paper deals with the stochastic stabilizability and passive control for a class of linear time-delay systems with Markov jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. A sufficient condition on stochastic stabilizability is established based on stability theory in stochastic differential equations. In terms of a set of coupled linear matrix inequalities, stochastic passive controllers are designed to stochastically stabilize the given systems with passive performance constraints. A numerical example demonstrates the effect of the proposed design approach.