This paper studies finite‐time annular domain stability (FTADS) and stabilization for stochastic Markovian switching systems driven by both Wiener and Poisson noises. Firstly, new sufficient conditions, based on the common parameter approach (CPA)/mode‐dependent parameter approach (MDPA), are presented to make the stochastic Markovian switching systems FTADS. Secondly, the finite‐time annular domain stabilization (FTAD‐stabilization) is discussed. The state feedback controller (SFC) and the dynamic output feedback controller (DOFC) are designed by CPA/MDPA, respectively, and some new sufficient conditions are given for the existence of these controllers. Moreover, an algorithm is presented to find the value ranges of some parameters, which shows the superiority of MDPA. Finally, a numerical example is supplied to verify the validity of our results.

中文翻译：

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由维纳和泊松噪声驱动的随机马尔可夫切换系统的有限时间环形域稳定性和镇定

本文研究了由维纳噪声和泊松噪声驱动的随机马尔可夫切换系统的有限时间环形域稳定性（FTADS）和稳定性。首先，提出了基于公共参数方法（CPA）/模式相关参数方法（MDPA）的新的充分条件，以使随机马尔可夫切换系统成为FTADS。其次，讨论了有限时间环形域稳定（FTAD稳定）。状态反馈控制器（SFC）和动态输出反馈控制器（DOFC）分别由CPA / MDPA设计，并为这些控制器的存在提供了一些新的充分条件。此外，提出了一种寻找某些参数取值范围的算法，这表明了MDPA的优越性。最后，提供了一个数字示例来验证我们的结果的有效性。