Sliding-Mode Control for Singular Markovian Jump Systems With Brownian Motion Based on Stochastic Sliding Mode Surface

Abstract

In this paper, the stabilization problems for singular Markovian systems with Brownian motion are studied by use of sliding mode control (SMC) with the jumping transfer matrix known, unknown, or partly unknown. At first, a new stochastic sliding mode surface (SSS) is introduced. The problem of state trajectories moving among several sliding mode surfaces can be settled perfectly. By use of the proposed SSS, the sliding mode dynamics of singular Markovian systems with Brownian motion is asymptotically mean square admissible and sufficient design conditions are derived in linear matrix inequalities. Second, by use of a new approach different from the normal Lyapunov method, an SMC law is provided to avoid the state trajectories escaping from the sliding mode surface. Finally, three numerical simulations and one practical simulation are provided to illustrate the validity of the proposed method.