This article investigates the event-triggered impulsive control (ETIC) problem for a class of nonlinear time-delay systems subject to exogenous disturbances. An original event-triggered mechanism (ETM) which utilizes the information of system state and external input is constructed based on Lyapunov function approach. To achieve the input-to-state stability (ISS) of the considered system, some sufficient conditions are presented, in which the underlying relationship among ETM, exogenous input, and impulse action is established. Furthermore, the possible Zeno behavior induced by the proposed ETM is excluded simultaneously. As an application, the design criterion of ETM and impulse gain is put forward for a class of impulsive control systems with delay according to the feasibility of some linear matrix inequalities (LMIs). Finally, two examples with numerical simulations are provided to confirm the effectiveness of the developed theoretical results, where the synchronization issue of delayed Chua’s circuit is considered.

中文翻译：

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非线性时滞系统输入状态稳定的事件触发脉冲控制

本文研究了一类受外生干扰的非线性时滞系统的事件触发脉冲控制 (ETIC) 问题。基于Lyapunov函数方法，构建了一种利用系统状态和外部输入信息的原始事件触发机制（ETM）。为了实现所考虑系统的输入状态稳定性（ISS），提出了一些充分条件，其中建立了 ETM、外源输入和脉冲作用之间的基本关系。此外，同时排除了所提出的 ETM 可能引发的 Zeno 行为。作为应用，根据某些线性矩阵不等式(LMI)的可行性，提出了一类时滞脉冲控制系统的ETM和脉冲增益的设计准则。最后，提供了两个数值模拟示例来证实所开发的理论结果的有效性，其中考虑了延迟蔡氏电路的同步问题。