This paper investigates the existence of non-impulsive unique solution and stochastic stability problems for the continuous-time linear rectangular descriptor Markov jump systems (DMJSs) at two cases. For every case, the sufficient and necessary conditions, in terms of strict linear matrix inequalities (LMIs), are eventually proposed to guarantee that the continuous-time linear DMJSs are column (row) regular, column (row) impulse-free, stochastically stable and have a unique solution. In addition, with some assumptions satisfied, the conditions obtained in this paper can simultaneously ensure that there is no impulse in the solution at the instant when the Markov process jumps. Finally, two examples are provided to demonstrate the effectiveness of the results.

本文研究了两种情况下连续时间线性矩形描述符Markov跳跃系统（DMJS）的非脉冲唯一解的存在性和随机稳定性问题。对于每种情况，最终都提出了严格的线性矩阵不等式（LMI）的充分必要条件，以确保连续时间线性DMJS为列（行）规则，列（行）无脉冲，随机稳定并有独特的解决方案。另外，在满足一些假设的前提下，本文获得的条件可以同时确保在马尔可夫过程跳跃的那一刻，解中没有脉冲。最后，提供了两个示例来证明结果的有效性。