Event-Triggered $H_{\infty }$ Control of Networked Control Systems With Distributed Transmission Delay

This article contributes to design an event-triggered <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> controller for networked control systems with network channel delay. First, the network channel delay is modeled as a distributed delay with a probability density function as its kernel. Then, the closed-loop event-triggered control system is established as a distributed delay system. To make full use of the delay probability distribution, the Lyapunov–Krasovskii functional is constructed with the distributed kernel. By applying the Lyapunov method, sufficient conditions for ensuring the stability of the closed-loop system with prescribed <inline-formula><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance are formulated in linear matrix inequalities. A numerical example shows that the proposed method is less conservative than some existing results considering delay distribution.