Abstract This paper investigates the finite-time stability (FTS) for a class of stochastic Markovian reaction-diffusion systems (SMRDSs). First, a boundary control strategy is put forward. Under the designed boundary controller, a sufficient condition of FTS for SMRDSs is provided based on the method of Lyapunov-Krasovskii functional combined with inequality techniques.When there exists the incompleteness of transition rate information, we further study the problem of SMRDSs with partially unknown transition rates (TRs) by adding a set of symmetric free matrices. An FTS criterion is also obtained for this case. Theoretical results show that the case of completely known TRs is the special case of partially unknown TRs. Finally, simulation examples are presented to verify the validity of our derived results.

中文翻译：

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具有通过边界控制的马尔可夫切换的随机反应扩散系统的有限时间稳定

摘要 本文研究了一类随机马尔可夫反应扩散系统 (SMRDS) 的有限时间稳定性 (FTS)。首先，提出了边界控制策略。在设计的边界控制器下，基于Lyapunov-Krasovskii泛函方法结合不等式技术，为SMRDSs提供了FTS的充分条件。通过添加一组对称自由矩阵来计算速率 (TR)。对于这种情况，还获得了 FTS 标准。理论结果表明，完全已知TRs的情况是部分未知TRs的特例。最后，通过仿真实例验证了我们推导结果的有效性。