H∞ control of Markov jump systems with time-varying delay and incomplete transition probabilities

Abstract

This paper addresses the H∞ control of continuous Markov jump systems with interval time-varying delay and incomplete transition probabilities. A linearization method is used to handle unknown transition probabilities. Meanwhile, the Wirtinger-based integral inequality and the reciprocally convex technique are adopted to deal with the time-varying delay. Additionally, a separating technique is employed to tackle the coupling among Lyapunov variable, system matrix and controller parameter. Based on these strategies, new sufficient conditions for the closed-loop system to be stochastically stable are formulated in the framework of linear matrix inequalities. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed method.