Static output feedback variable structure control for Markov jump systems

In this paper, the static output feedback variable structure control for Markov jump systems is discussed. First, the sliding mode dynamics and the switching surface are treated as a descriptor Markov jump system. Based on stochastic stability theory of descriptor Markov jump systems, a linear matrix inequality (LMI) sufficient condition which guarantees the stochastic stability of the sliding mode dynamics and the existence of the switching surface is given. Then, by using LMI, the design method of a static output feedback variable structure controller is given, which guarantees that the closed-loop system is stochastically stable, and the state trajectories of the closed-loop system are convergent to the switching surface in finite time. Last, a numerical example is given to show the correctness and effectiveness of the proposed method.