Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

Jian Xiao,Jie Zhou,Jiayao Peng,Tao Zhao,Chang Che

doi:10.1155/2018/3542352

Abstract

This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S) fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs) are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

Highlights

In recent years, T-S fuzzy system has become a very active research direction in the fields of fuzzy control [1,2,3,4,5,6,7,8]
This paper focuses on the problem of nonlinear systems with input and state delays
The existing results are still very conservative due to the form of LyapunovKrasovskii functional (LKF), and constructing new LKF with more system information is a challenging issue to reduce the conservativeness of stability analysis for T-S fuzzy time-delay system

Summary

Introduction

T-S fuzzy system has become a very active research direction in the fields of fuzzy control [1,2,3,4,5,6,7,8]. Many valuable results on stability analysis, controller design, filter design, and fault detection of T-S fuzzy systems have been widely reported in [9,10,11,12,13,14,15,16,17,18,19]. LyapunovKrasovskii functional (LKF) technique is an effective method to handle stability analysis and controller design of T-S fuzzy time-delay system. There are two main relaxed techniques for TS fuzzy time-delay system, for example, constructing new LKF with more system information and using new bounding inequalities. The existing results are still very conservative due to the form of LKF, and constructing new LKF with more system information is a challenging issue to reduce the conservativeness of stability analysis for T-S fuzzy time-delay system

Objectives

Results

Conclusion