The asynchronous sliding mode control (SMC) problem is investigated for networked Markovian jump Lur’e systems, in which the information of system modes is unavailable to the sliding mode controller but could be estimated by a mode detector via a hidden Markov model (HMM). In order to mitigate the burden of data communication, an event-triggered protocol is proposed to determine whether the system state should be released to the controller at certain time-point according to a specific triggering condition. By constructing a novel common sliding surface, this paper designs an event-triggered asynchronous SMC law, which just depends on the hidden mode information. A combination of the stochastic Lur’e-type Lyapunov functional and the HMM approach is exploited to establish the sufficient conditions of the mean square stability with a prescribed ${H}_{\infty }$ performance and the reachability of a sliding region around the specified sliding surface. Moreover, the solving algorithm for the control gain matrices is given via a convex optimization problem. Finally, an example from the dc motor device system is provided.

中文翻译：

---

隐藏模式检测下马尔可夫跳跃诱饵系统滑模控制的事件触发方法

针对网络化马尔可夫跳跃 Lur'e 系统研究了异步滑模控制 (SMC) 问题，其中系统模式的信息对滑模控制器不可用，但可以由模式检测器通过隐马尔可夫模型 (HMM) 估计. 为了减轻数据通信的负担，提出了一种事件触发协议，根据特定的触发条件确定是否应该在某个时间点将系统状态发布给控制器。通过构造一个新颖的公共滑动面，本文设计了一种仅依赖于隐藏模式信息的事件触发异步 SMC 定律。随机 Lur'e 型 Lyapunov 泛函和 HMM 方法的组合被用来建立均方稳定性的充分条件，具有规定的 ${H}_{\infty }$ 性能和周围滑动区域的可达性指定的滑动面。此外，通过凸优化问题给出了控制增益矩阵的求解算法。最后，提供了一个来自直流电机设备系统的例子。