Abstract The paper investigates the issue of mixed H∞ and dissipative asynchronous controller design for a class of Markov jump singularly perturbed systems (MJSPSs). A suitable dynamic event-triggered rule is offered to further mitigate the transmission burden of communication network. Since the mode information of Markov chain is extremely difficult to get, an asynchronous controller is well constructed. Hence, a hidden Markov model (HMM) is chosen to describe the non-synchronous facts between states of the original Markov chain and the constructed non-synchronous controller. Resorting to the Lyapunov functional concerning the internal dynamic variable, sufficient conditions of stochastically stable with a certain mixed H∞ and dissipative performance for the resulting closed-loop MJSPSs are offered. Based on the LMI technique, the design framework of asynchronous controller and the dynamic event-triggered rule are given in a unified way. Lastly, a modified DC motor model is offered to demonstrate the superiority of the proffered method.

中文翻译：

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马尔可夫跳跃奇异摄动系统的基于动态事件的混合H∞和耗散异步控制

摘要 本文研究了一类马尔可夫跳跃奇异摄动系统（MJSPS）的混合H∞和耗散异步控制器设计问题。提供了合适的动态事件触发规则，以进一步减轻通信网络的传输负担。由于马尔可夫链的模式信息极难获取，所以很好地构造了一个异步控制器。因此，选择隐马尔可夫模型（HMM）来描述原始马尔可夫链和构造的非同步控制器状态之间的非同步事实。借助关于内部动态变量的 Lyapunov 泛函，提供了具有一定混合 H∞ 的随机稳定的充分条件以及所得闭环 MJSPS 的耗散性能。基于LMI技术，统一给出了异步控制器的设计框架和动态事件触发规则。最后，提供了一个改进的直流电机模型来证明所提供方法的优越性。