Delay-Dependent H∞ Control for T-S Fuzzy Systems with Local Nonlinear Models: An LMI Approach

Zhile Xia

doi:10.1155/2020/2301085

Abstract

This paper studies the stabilization design scheme with H∞ performance for a large class of nonlinear discrete-time systems. The system under study is modeled by Takagi-Sugeno (T-S) model with local nonlinearity and state delay. First, the model is changed into an equivalent fuzzy switching model. And then, according to projection theorem and piecewise Lyapunov function (PLF), two new H∞ control methods are proposed for fuzzy switched systems, which consider the time delay information of the system. Finally, the relationship among all fuzzy subsystems is considered. Because the results are only expressed by a series of linear matrix inequalities (LMIs), the controller can be directly designed by the linear matrix inequalities toolbox of MATLAB.

Highlights

As we all know, the T-S fuzzy method is a kind of common and very effective tool for approaching the discrete-time nonlinear complex system [1]
In [2, 3], it was shown that coupled chaotic systems are a special class of complex systems, which can be processed by the T-S method [4, 5]
In order to increase the feasible region of matrix inequalities, a piecewise Lyapunov function (PLF) is proposed in [15, 16], which studied the filter problem for the T-S model with delay

Summary

Introduction

The T-S fuzzy method is a kind of common and very effective tool for approaching the discrete-time nonlinear complex system [1]. Erefore, it is very important to study the asymptotic stability and controller design of the T-S fuzzy model [11,12,13]. In order to increase the feasible region of matrix inequalities, a piecewise Lyapunov function (PLF) is proposed in [15, 16], which studied the filter problem for the T-S model with delay.

Results

Conclusion