Further Stability Analysis of Time-Delay Systems with Nonlinear Perturbations

Jie Sun,Jing Zhang

doi:10.1155/2017/5941757

Abstract

In this study, we focus on stability analysis for systems with time-varying delay and nonlinear perturbations. In order to cut down the conservatism of the existing stability criteria, we utilize the triple integral forms of Lyapunov-Krasovskii functional (LKF). In addition, by using single and double integral forms of Wirtinger-based inequality, we overcome some conservatism which come from Jensen’s inequality. Three well-known numerical examples are given at the end. Compared with some existing results, our results have less conservatism.

Highlights

We focus on stability analysis for systems with time-varying delay and nonlinear perturbations
Time-delay has attracted a lot of interests because it is widely encountered in communication systems, neural networks, economic systems, biological systems, and networked control systems [1,2,3,4,5,6]
The maximum allowable delay bound (MADB) of the time-delay can measure the conservatism of stability criterion

Summary

Introduction

Time-delay has attracted a lot of interests because it is widely encountered in communication systems, neural networks, economic systems, biological systems, and networked control systems [1,2,3,4,5,6]. We focus on cutting down the conservatism of stability criterion. The maximum allowable delay bound (MADB) of the time-delay can measure the conservatism of stability criterion. We can get the larger MADB of time-varying delay according to the stability criterion with less conservatism. To cut down the conservatism, Wirtingerbased integral inequality [7], which can be used to obtain much tighter lower bound of single integral terms, was proposed. In a lot of recent literatures [9,10,11], researchers only utilize single and double integral forms of LKF to derive delaydependent stability criterion. We introduce the triple integral forms of LKF to cut down the conservatism. The superscript T means the transpose of a matrix; col{⋅} denotes the column vector

Problem Formulation and Preliminaries

Stability Criterion

Numerical Examples

Methods

Findings

Conclusion