Abstract This paper investigates the problem of H ∞ control for continuous-time singular Markovian jump systems in the event-triggered framework. Different from the traditional event-triggered control systems, we introduce a dynamic event-triggered mechanism to monitor the data transmission from system plant to controller, which can lead to a smaller amount of data transmission and thus a higher efficiency of the communication resource. A positive lower bound on the inter-event intervals is proved to exist, which implies the exclusion of the Zeno behaviour. Based on this, sufficient conditions are obtained to ensure that the closed-loop system is stochastically admissible with an H ∞ disturbance attenuation. Then both the state feedback controller and the dynamic event-triggered mechanism are designed based on the analysis result. The dynamic event-triggered control is also extended to the system with network-induced delays due to the inevitability of time delay in practical transmission. Finally, two examples are provided to demonstrate the effectiveness and superiority of the proposed new design scheme.

中文翻译：

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基于动态事件触发控制策略的奇异马尔可夫跳跃系统的稳定性和镇定性

摘要 本文研究了事件触发框架下连续时间奇异马尔可夫跳跃系统的H ∞ 控制问题。与传统的事件触发控制系统不同，我们引入了动态事件触发机制来监控从系统设备到控制器的数据传输，这可以减少数据传输量，从而提高通信资源的效率。事件间间隔的正下限被证明存在，这意味着排除了 Zeno 行为。在此基础上，获得了足够的条件来确保闭环系统是随机允许的，具有 H ∞ 扰动衰减。然后根据分析结果设计了状态反馈控制器和动态事件触发机制。由于实际传输中时延的不可避免性，动态事件触发控制也扩展到具有网络引起的时延的系统。最后，提供了两个例子来证明所提出的新设计方案的有效性和优越性。