Robust H∞ finite-time control of switched stochastic systems with time delay

In this paper, we consider the problem of robust H∞ finite-time control for a class of switched stochastic systems with time delay. Firstly, the concept of finite-time boundedness is extended to switched stochastic systems. Then, based on the average dwell time method, some sufficient conditions under which switched stochastic systems are finite-time stochastically bounded are given. Moreover, finite-time H∞ performance is investigated, and robust H∞ controller is designed to guarantee that the corresponding closed-loop system is finite-time stochastically bounded with H∞ performance. All conditions are formulated in terms of a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed approach.