Abstract This work investigates the problem of finite-time stochastic boundedness for a class of Markovian jump systems by synthesizing the sliding mode control and the transition rate matrix. First, a sufficient condition on the transition rate matrix is derived to guarantee the finite-time stochastic boundedness of the unforced Markovian jump systems. Moreover, a hybrid design scheme integrating the transition rate matrix with the sliding mode controller is synthesized such that the closed-loop systems are ensured to be finite-time stochastically bounded over both reaching phase and sliding motion phase. Finally, two examples are exploited to illustrate the proposed method.

中文翻译：

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马尔可夫跳跃系统的有限时间随机有界：一种基于滑模的混合设计方法

摘要 本文通过综合滑模控制和跃迁率矩阵研究一类马尔可夫跳跃系统的有限时间随机有界问题。首先，推导出转移率矩阵的充分条件，以保证非受迫马尔可夫跳跃系统的有限时间随机有界性。此外，将过渡速率矩阵与滑模控制器相结合的混合设计方案被综合起来，从而确保闭环系统在到达阶段和滑动运动阶段都是有限时间随机有界的。最后，利用两个例子来说明所提出的方法。