Delay-dependent passive control for stochastic differential systems with Markov switching and time delay

The problem of passive analysis and control for stochastic differential systems with Markov switching and time delay is investigated. A new conception of passivity is presented, and the condition for delay-dependent passiveness of such stochastic systems is obtained by constructing a new type of Lyapunov-Krasovskii function, employing model transformation and Newton-Leibniz equality and slack matrix technique. Based on this condition, delay-dependent passive controllers for such stochastic systems are presented. The proposed results are formulated in terms of linear matrix inequalities (LMIs), which can be efficiently solved by standard convex optimization algorithms. And, a numerical example shows the effectiveness of the proposed method.