Finite-Time Control for Nonlinear Systems with Time-Varying Delay and Exogenous Disturbance

Yanli Ruan,Tianmin Huang

doi:10.3390/sym12030447

Abstract

This paper is concerned with the problem of finite-time control for nonlinear systems with time-varying delay and exogenous disturbance, which can be represented by a Takagi–Sugeno (T-S) fuzzy model. First, by constructing a novel augmented Lyapunov–Krasovskii functional involving several symmetric positive definite matrices, a new delay-dependent finite-time boundedness criterion is established for the considered T-S fuzzy time-delay system by employing an improved reciprocally convex combination inequality. Then, a memory state feedback controller is designed to guarantee the finite-time boundness of the closed-loop T-S fuzzy time-delay system, which is in the framework of linear matrix inequalities (LMIs). Finally, the effectiveness and merits of the proposed results are shown by a numerical example.

Highlights

During the past several decades, the control problem of nonlinear systems has attracted considerable attention [1,2,3,4,5,6] as various practical systems are essentially nonlinear and cannot be simplified into a linear model
Many fuzzy logic control approaches have been proposed for the control problem of nonlinear systems
Many significant and interesting results on stability analysis and the control synthesis of T-S fuzzy time-delay systems have been developed in the literature [8,9,10,11,12,13,14,15]

Summary

Introduction

During the past several decades, the control problem of nonlinear systems has attracted considerable attention [1,2,3,4,5,6] as various practical systems are essentially nonlinear and cannot be simplified into a linear model. Many fuzzy logic control approaches have been proposed for the control problem of nonlinear systems. The Takagi–Sugeno (T-S) fuzzy model, developed in [7], is an important tool to approximate complex nonlinear systems by combining the fruitful linear system theory and the flexible fuzzy logic approach. Many significant and interesting results on stability analysis and the control synthesis of T-S fuzzy time-delay systems have been developed in the literature [8,9,10,11,12,13,14,15]

Objectives

Results

Conclusion