Analysis and Synthesis of Uncertainty Singular Markov Switched Systems Based on the Sliding Mode Control

In this paper, a class of singular Markov switched systems with mismatched norm-bounded uncertainties and external disturbances is considered. A sufficient condition guaranteeing the existence of linear switching surface is given based on the linear matrix inequality method (LMIs). It is shown that the sliding mode dynamic on the switching surface is stochastically stable and satisfies performance. A sliding mode controller is designed to guarantee that the system trajectory is convergent to the linear switching surface. A numerical example is given to illustrate the effectiveness of the proposed method.