Sliding-Mode Control for Singular Markovian Jump Systems With Brownian Motion Based on Stochastic Sliding Mode Surface
针对带布朗运动的奇异马尔可夫跳跃系统，提出一种新随机滑模面，解决多滑模面间状态轨迹移动问题，并设计滑模控制律确保系统均方渐近可容许，适用于转移矩阵已知、未知或部分未知情形。
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.