Fuzzy-Model-Based Robust $H_{\infty}$ Design of Nonlinear Packetized Networked Control Systems

Abstract

This paper is concerned with the fuzzy-model-based robust $H_{\infty}$ design of a nonlinear packetized networked control system with time-varying transmission delays and transmission intervals based on a delay-distribution approach combined with an improved Lyapunov–Krasovskii method. By the delay-distribution approach, the real-time distribution of input delays is described as a dependent and nonidentically distributed process, and the nonlinear packetized networked control system is modeled as a novel randomly switched Takagi–Sugeno fuzzy system with multiple uncertain input-delay subsystems. The improved Lyapunov–Krasovskii method is proposed to more rationally exploit the real-time distribution of input delays and the synchronous membership functions of the Takagi–Sugeno fuzzy models of the plant and the packetized parallel distributed compensation scheme. New de- lay-distribution-dependent sufficient conditions are derived for the deterministic robust exponential stability and $H_{\infty}$ performance of the overall system. The resulting controller design method of the packetized parallel distributed compensation scheme is equivalent to an iterative linear optimization algorithm with linear matrix inequality constraints. Detailed numerical examples are presented to substantiate the effectiveness and advantage of our theoretical results.