Periodic event-triggered control (PETC) evaluates triggering conditions only at periodic sampling times, based on which it is decided whether the controller needs to be updated. This article investigates the global stabilization of nonlinear systems that are affected by external disturbances under PETC mechanisms. Sufficient conditions are provided to ensure the resulting closed-loop system is input-to-state stable (ISS) for the state feedback and the observer-based output feedback configurations separately. The sampling period and the triggering functions are chosen such that the ISS-Lyapunov function of continuous dynamics is also the ISS-Lyapunov function of the overall system. Based on that, sufficient conditions in the form of linear matrix inequalities are provided for the PETC design of incrementally quadratic nonlinear systems. Two simulation examples are provided to illustrate the effectiveness of the proposed method.

中文翻译：

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增量二次非线性系统的周期性事件触发控制

周期性事件触发控制 (PETC) 仅在周期性采样时间评估触发条件，并据此决定是否需要更新控制器。本文研究了在 PETC 机制下受外部扰动影响的非线性系统的全局稳定性。提供了足够的条件以确保所得闭环系统对于状态反馈和基于观测器的输出反馈配置分别是输入到状态稳定 (ISS)。选择采样周期和触发函数，使得连续动力学的 ISS-Lyapunov 函数也是整个系统的 ISS-Lyapunov 函数。在此基础上，为增量二次非线性系统的PETC设计提供了线性矩阵不等式形式的充分条件。