A new design of sliding mode control for Markovian jump systems based on stochastic sliding surface

With the jumping transfer matrix unknown, partly unknown or known, the stabilization problems for Markovian jump systems are considered by use of sliding mode control method in this paper. Firstly, a new integral sliding mode surface named stochastic sliding surface (SSS) is introduced. The SSS is characterized that the state trajectories are on the sliding surface all the time even at the time of system switching. So the problem of the state trajectories moving among several sliding surfaces by use of traditional sliding mode control method is settled perfectly. Based on the new sliding mode surface, sufficient conditions for the stability of the sliding mode dynamics are derived. Secondly, sliding mode control (SMC) law is synthesized to avoid the state trajectories escaping from the surface. Finally, some simulations are provided to illustrate the validity of the proposed method.