Abstract: For discrete-time Markov jump linear systems with truncated Gaussian transition probabilities (GTP), the mean and the variance of GTP based state feedback controller and stabilizable region are investigated in this paper. To reduce the conservativeness of the existing results, we introduce the mean and the variance of TGTP into the design of the controller. Furthermore, to reveal the essential influence of system parameters, the mean and the variance of TGTP on controller design, the explicit solution of stabilizable domain is derived based on the approach of matrix eigenvalues boundary. Finally, several examples are presented to demonstrate the effectiveness of the proposed method.

Key words: Discrete Markov jump linear system, truncated Gaussian transition probability, stabilizable condition, stabilizable region

摘要： 针对转移概率服从高斯分布的离散Markov跳变系统，研究基于截断高斯转移概率均值和方差信息的状态反馈控制器设计以及可镇定域求解问题。首先，将截断高斯转移概率的均值和方差信息引入控制器的设计，降低了已有设计方法的保守性。进一步，为了揭示系统参数、截断高斯转移概率的均值和方差对系统可镇定域的影响，采用矩阵特征值估计方法，求解闭环系统可镇定域的解析表达式。最后仿真示例对所提控制算法进行了验证。

关键词: 离散Markov跳变系统, 截断高斯转移概率, 可镇定条件, 镇定域求解