Sliding Mode Control of Uncertain Switched Systems with Partly Known Sojourn Probabilities

This paper is concerned with the sliding mode control (SMC) problem for a class of uncertain switched systems subject to partly known sojourn probabilities. The sojourn probability is the probability of a switched system staying in each subsystem, which may be available or unavailable. A key issue is how to design a sliding mode controller to guarantee the stability performance of the reconstructed switched systems subject to the partly known sojourn probabilities. To this end, by using a set of stochastic variables, the switched system model is reconstructed with partly known sojourn probabilities. And then, the sliding mode control law is constructed to ensure the reachability of the designed common sliding surface. Furthermore, the sufficient condition is derived to ensure the mean-square stability of the closed-loop system under the partly unknown sojourn probabilities. Finally, a numerical example is provided to illustrate the proposed method.