In this article, passivity-based sampled-data control for Markovian jump systems (MJSs) with stochastic sampling is conducted by virtue of the looped-functional approach. First, based on the input delay approach, the MJS under stochastic sampled-data control is modeled as a time-varying continuous-time system with a random variable. Second, a time-dependent looped-functional is developed, which only requires its positive definiteness at the sampling instants and takes full use of the state information. Moreover, a free-matrix-based integral inequality is used to derive some less conservative passivity conditions expressed in terms of linear matrix inequality (LMIs). Meanwhile, a design algorithm for the mode-dependent stochastic sampled-data controller is provided. A numerical example is given to demonstrate the validity and superiority of the proposed analysis method.

中文翻译：

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通过循环函数方法对马尔可夫跳跃系统进行基于被动的随机采样数据控制

在本文中，利用循环函数方法对具有随机采样的马尔可夫跳跃系统 (MJS) 进行了基于被动的采样数据控制。首先，基于输入延迟方法，随机采样数据控制下的 MJS 被建模为具有随机变量的时变连续时间系统。其次，开发了一个时间相关的循环泛函，它只需要在采样时刻的正定性并充分利用状态信息。此外，基于自由矩阵的积分不等式用于推导出一些不太保守的被动条件，用线性矩阵不等式 (LMI) 表示。同时，提出了模态相关随机采样数据控制器的设计算法。