In this paper, the problems of finite-time stability analysis and finite-time stabilization are investigated for Markovian jump linear systems with incomplete transition descriptions. Two sufficient conditions are proposed to guarantee that the system states do not exceed a certain threshold in mean-square sense during a specified time interval for the continuous-time Markovian jump linear systems with partly unknown transition rates and the discrete-time Markovian jump linear systems with partly unknown transition probabilities, respectively. On the basis of the above results, two state feedback controllers are developed to solve the finite-time stochastic stabilization problems of the considered systems in continuous-time domain and discrete-time domain, respectively. For the sake of computational convenience, all the conditions are cast in the format of linear matrix inequalities (LMIs). The main feature of the proposed methods is that the total number of LMIs is much less than that in some existing results. Thus, the solution of the finite-time controllers is more concise both in theory and in engineering. In the end, the validity of the developed theoretical results are demonstrated by two illustrative examples.

本文研究了具有不完全过渡描述的马尔可夫跳跃线性系统的有限时间稳定性分析和有限时间镇定问题。对于跃迁率部分未知的连续时间马尔可夫跳跃线性系统和离散时间马尔可夫跳跃线性系统，提出了两个充分条件来保证系统状态在指定时间间隔内不超过均方意义上的某个阈值分别具有部分未知的转移概率。在上述结果的基础上，分别开发了两种状态反馈控制器来解决所考虑系统在连续时域和离散时域中的有限时间随机镇定问题。为了计算方便，所有条件都以线性矩阵不等式 (LMI) 的格式进行转换。所提出方法的主要特点是LMI的总数比现有的一些结果少得多。因此，有限时间控制器的求解在理论上和工程上都更加简洁。最后，通过两个说明性例子证明了所开发的理论结果的有效性。