\(H_{\infty}\) PID Control for Discrete-time Network Control Systems with Redundant Channels under Dynamic Event-triggered Scheme

Abstract

This paper is concerned with the \(H_{\infty}\) proportional-integral-derivative (PID) control problem for a class of discrete-time networked control systems (NCSs). First, a dynamic event-triggered control (DETC) scheme has been introduced to save the constrained network bandwidth of networked control systems. In addition, in order to reduce the probability of data packet loss and further improve the reliability of network communication, a redundant channels transmission mechanism has been constructed during the sensor transmission process. Considering that the system state may not be obtained directly, an observer has been added when designing a closed-loop system to observe the system state. Then, according to the closed-loop system construction, with the help of Lyapunov function and through a series of derivations, some sufficient conditions are established to guarantee the exponentially stability and the prescribed \(H_{\infty}\) performance for the controlled system. Meanwhile, under the condition that the system satisfies the \(H_{\infty}\) performance, the gains of the observer and PID controller can be derived by solving linear matrix inequalities (LMIs). Finally, a simulation example is presented to demonstrate the validity of the proposed method.