Abstract: A variable structure control method is proposed for uncertain Markov jump systems based on sliding sector method. The sliding sector of stochastic Markov jump systems is firstly defined, and then the design method of the sliding sector is given based on linear matrix inequality technique. Subsequently, the variable structure control law is established. It shows in theory that the control law can guarantee the quadratic stability of the stochastic Markov jump uncertain system and the chattering problem is avoided. Finally, a numerical example verifies the effectiveness of the control scheme.

Key words: stochastic systems, Markov jump, variable structure control, sliding sector

摘要： 采用滑动扇区方法，研究了不确定随机马尔可夫跳变系统的变结构控制设计问题。首先给出随机马尔可夫跳变系统滑动扇区的定义，然后基于线性矩阵不等式技术，提出一种滑动扇区及变结构控制律设计方法。经过理论证明该控制律能够确保随机马尔可夫跳变不确定系统二次稳定，并有效地抑制抖振。最后数值仿真算例验证了控制方案的有效性。

关键词: 随机系统, 马尔可夫跳变, 变结构控制, 滑动扇区