中文摘要：

利用直接法对转移概率是部分未知的，并且具有执行器饱和现象的随机Markov切换系统进行稳定性分析．通过引入自由连接权矩阵降低系统的保守性．首先，针对此类随机Markov切换系统，充分考虑转移概率中元素之间的特性，通过构建参数依赖型Lyapunov函数，并设计观测器确保闭环饱和系统的随机稳定性．然后，在线性矩阵不等式的框架下，得到均方意义下的最大不变吸引域，并将其归结为求解一组线性矩阵不等式的可行性问题．最后，数值仿真算例验证本方法的有效性．

英文摘要：

The direct approach was used to study the stochastic Markov switching system with partly unknown transition probabilities and actuator saturation considering the problem of stochastic stability analysis. Through using free connection weight matrix, the conservation of the system would be decreased. Firstly, for stochastic Markov switching systems, by considering the properties of the relationship between the transition probabilities, the observer was designed to guarantee the stochastic stability of the closed-loop saturated system based on the parameter- dependent Lyapunov function. And then, the largest contraction invariant set in the mean square sense was proposed in the framework of linear matrix inequalities （LMIs）. Finally, a numerical example was given to demonstrate the effectiveness of the method.