Event-Triggered Control for Linear Systems With Time-Varying Delays: An Improved Halanay Technique

This article investigates an event-triggered control for linear systems with process time-varying delays. An exponential absolute event-trigger (ET) is designed for reducing the data transmission burden of the communication network. The decay rate and the absolute threshold of the ET can be prior-specified, it provides a convenient method to regulate the event-triggering behaviors and the convergence rate of measurement error. Utilizing the available state information, a nonperiodical discrete-time feedback control is proposed. By an auxiliary exponential function, the constant Halanay equation is proved to be effective to the time-varying delayed system. A concise controller design method is presented in terms of low-dimensional linear matrix inequality (LMI). Significantly, the qualitative relationship between the maximal allowable bound of time delays with the minimal decay rate of the closed-loop system is presented. By the proposed ET-based control, the uniform ultimate bound (UUB) of the closed-loop system is guaranteed. Given positive absolute threshold of the ET, the Zeno behavior can be thoroughly excluded. Numerical examples are provided to demonstrate the effectiveness of the proposed method.