New results on H∞ control for stochastic switched systems with delay

In this paper, a sojourn-probability-dependent method is proposed to investigate H_∞ control for a class of switched systems with input delays. The considered system has the following characteristics: 1) it is a switched system consisting of a set of subsystems; 2) sojourn probabilities (i.e. the probability of switched systems staying in each subsystem) are assumed to be known a prior; and 3) there are input delays in each subsystem. By using the sojourn probability information, a new type of switched system model is built, which can cover some of the existing ones as special cases and has many applications in practical systems. By using the Lyapunov functional method, mean square stability criteria are obtained for switched systems. Then H_∞ controller feedback gains are derived by using the cone complement linearization method. An inverted pendulum system is given to demonstrate the effectiveness and applicability of the proposed method.