This paper deals with the problem of dissipativity-based asynchronous fault detection (FD) for Takagi–Sugeno fuzzy Markov jump systems with network data dropouts. It is assumed that data dropouts happen intermittently from the plant to the FD filter, which is described by Bernoulli process. The hidden Markov model is employed to describe the asynchronous phenomenon between the plant and filter. Based on Lyapunov theory, a sufficient condition is developed to guarantee that the FD system is stochastically stable with strictly dissipative performance. By choosing an appropriate Lyapunov function with the slack matrix technique and Finsler's Lemma, two approaches are proposed to compute filter gains by solving linear matrix inequalities. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed design methods.

中文翻译：

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马尔可夫跳跃非线性系统的网络故障检测

本文讨论了具有网络数据丢失的 Takagi-Sugeno 模糊马尔可夫跳跃系统的基于耗散性的异步故障检测 (FD) 问题。假设数据丢失从工厂到 FD 过滤器间歇性发生，这由伯努利过程描述。采用隐马尔可夫模型来描述被控对象与滤波器之间的异步现象。基于李雅普诺夫理论，开发了一个充分条件来保证 FD 系统随机稳定且具有严格的耗散性能。通过使用松弛矩阵技术和 Finsler 引理选择合适的 Lyapunov 函数，提出了两种通过求解线性矩阵不等式来计算滤波器增益的方法。最后，提供了一个例子来说明所提出的设计方法的有用性和有效性。