Passivity-based control of a class of Markovian jump delayed systems

This paper is concerned with the passivity-based control problem for jumping delayed systems with two separable Markov processes. Such two processes appear in the open-loop system and control action, respectively. By utilizing a new Markovian switched Lyapunov functional and the reciprocal projection lemma, a delay-dependent condition is obtained for the existence of solutions to the problem in term of linear matrix inequalities. Based on this condition, the expression of the desired controllers is presented. A numerical example is provided to demonstrate the effectiveness of the proposed results.