This paper deals with the control of a class of stochastic multi-timescale systems, called Markov jump singularly perturbed systems. The hidden semi-Markov model is introduced to handle the situation when system modes are unavailable in semi-Markov systems. Such a model is assumed deficient, that is, it lacks knowledge about the emission probability, transition probability, and probability density function of the sojourn time. It is a more general case compared with works conducted with perfect transition information. Depending on whether a fast or slow sampling rate is used, the resulting discrete-time singularly perturbed system is modeled differently, for both of which the controller design is conducted. Furthermore, criteria expressed in terms of linear matrix inequalities (LMIs) are developed that guarantee the -error mean-square stability. An approach to estimate the upper bound on -error with incomplete information is provided, meanwhile, the relationship between system performance and the upper of singular perturbation parameter is also presented. Finally, two simulation examples using real-world systems are provided to corroborate the validity as well as the practical merits of the results.

中文翻译：

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[公式省略]利用缺陷隐半马尔可夫模型控制奇扰动系统

本文讨论一类随机多时间尺度系统的控制，称为马尔可夫跳跃奇异扰动系统。引入隐半马尔可夫模型来处理半马尔可夫系统中系统模式不可用的情况。这样的模型被假设是有缺陷的，即它缺乏关于停留时间的发射概率、转移概率和概率密度函数的知识。与使用完美过渡信息进行的工作相比，这是一个更一般的情况。根据使用快采样率还是慢采样率，对所得离散时间奇异扰动系统进行不同的建模，并针对这两种系统进行控制器设计。此外，还制定了以线性矩阵不等式（LMI）表示的标准，以保证误差均方稳定性。提出了一种在不完全信息的情况下估计误差上限的方法，同时给出了系统性能与奇异扰动参数上限之间的关系。最后，提供了两个使用真实系统的仿真示例来证实结果的有效性和实用价值。