In this article, the problem of the asynchronous fault detection (FD) observer design is discussed for 2-D Markov jump systems (MJSs) expressed by a Roesser model. In general, the FD observer cannot work synchronously with the system, that is, the mode of the observer varies with the mode of the system in line with some conditional transitional probabilities. For dealing with this difficult point, a hidden Markov model (HMM) is employed. Then, combining the H∞H_{\infty } attenuation index and H_H_{\_{}} increscent index, a multiobjective solution to the FD problem is formed. In terms of linear matrix inequality technology, sufficient conditions are gained to guarantee the existence of the asynchronous FD. Simultaneously, an asynchronous FD algorithm is generated to acquire the optimal performance indices. Finally, a numerical example concerned with the Darboux equation is demonstrated to exhibit the soundness of the developed approach.

中文翻译：

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二维马尔可夫跳跃系统的异步故障检测观测器


在本文中，讨论了 Roesser 模型表示的二维马尔可夫跳跃系统 (MJS) 的异步故障检测 (FD) 观测器设计问题。一般来说，FD观测器不能与系统同步工作，即观测器的模态随着系统模态的变化而变化，符合一定的条件转移概率。为了解决这个难点，采用了隐马尔可夫模型（HMM）。然后，结合H∞H_{\infty }衰减指数和H_H_{\_{}}增量指数，形成FD问题的多目标解。利用线性矩阵不等式技术，获得了保证异步FD存在的充分条件。同时，生成异步FD算法以获得最佳性能指标。最后，一个与达布方程相关的数值例子证明了所开发方法的合理性。