Robust H∞ control for switched systems with input delays: A sojourn-probability-dependent method

In this paper, a sojourn-probability-dependent method is proposed to investigate the robust 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 (or partly known) a prior; and (3) there are input delays and parameter uncertainties in each subsystem. By using the sojourn probability information, a new type of switched system model is built. By using the Lyapunov functional method, the robust mean square stability criteria are obtained for switched systems under two conditions: (A) all sojourn probabilities of the subsystems are known; (B) only partly sojourn probabilities are known. Then the robust H∞ controller feedback gains are derived by using the cone complement linearization method. An inverted pendulum system and a numerical example are given to demonstrate the effectiveness and applicability of the proposed method.