Relaxed conditions for stability of time-varying delay systems

Tae H. Lee; Ju H. Park; Shengyuan Xu

doi:10.1016/j.automatica.2016.08.011

Relaxed conditions for stability of time-varying delay systems

Tae H. Lee
, Ju H. Park
, Shengyuan Xu

Division of Electronic Engineering

Yeungnam University
Nanjing University of Science and Technology

Research output: Contribution to journal › Journal article › peer-review

260 Scopus citations

Abstract

In this paper, the problem of delay-dependent stability analysis of time-varying delay systems is investigated. Firstly, a new inequality which is the modified version of free-matrix-based integral inequality is derived, and then by aid of this new inequality, two novel lemmas which are relaxed conditions for some matrices in a Lyapunov function are proposed. Based on the lemmas, improved delay-dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality (LMI). Two numerical examples are given to describe the less conservatism of the proposed methods.

Original language	English
Pages (from-to)	11-15
Number of pages	5
Journal	Automatica
Volume	75
DOIs	https://doi.org/10.1016/j.automatica.2016.08.011
State	Published - 2017.01.1

Keywords

Free-matrix-based integral inequality
Relaxed condition
Stability
Time-varying delay

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10.1016/j.automatica.2016.08.011

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title = "Relaxed conditions for stability of time-varying delay systems",

abstract = "In this paper, the problem of delay-dependent stability analysis of time-varying delay systems is investigated. Firstly, a new inequality which is the modified version of free-matrix-based integral inequality is derived, and then by aid of this new inequality, two novel lemmas which are relaxed conditions for some matrices in a Lyapunov function are proposed. Based on the lemmas, improved delay-dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality (LMI). Two numerical examples are given to describe the less conservatism of the proposed methods.",

keywords = "Free-matrix-based integral inequality, Relaxed condition, Stability, Time-varying delay",

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T1 - Relaxed conditions for stability of time-varying delay systems

AU - Lee, Tae H.

AU - Park, Ju H.

AU - Xu, Shengyuan

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this paper, the problem of delay-dependent stability analysis of time-varying delay systems is investigated. Firstly, a new inequality which is the modified version of free-matrix-based integral inequality is derived, and then by aid of this new inequality, two novel lemmas which are relaxed conditions for some matrices in a Lyapunov function are proposed. Based on the lemmas, improved delay-dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality (LMI). Two numerical examples are given to describe the less conservatism of the proposed methods.

AB - In this paper, the problem of delay-dependent stability analysis of time-varying delay systems is investigated. Firstly, a new inequality which is the modified version of free-matrix-based integral inequality is derived, and then by aid of this new inequality, two novel lemmas which are relaxed conditions for some matrices in a Lyapunov function are proposed. Based on the lemmas, improved delay-dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality (LMI). Two numerical examples are given to describe the less conservatism of the proposed methods.

KW - Free-matrix-based integral inequality

KW - Relaxed condition

KW - Stability

KW - Time-varying delay

UR - https://www.scopus.com/pages/publications/84994043937

U2 - 10.1016/j.automatica.2016.08.011

DO - 10.1016/j.automatica.2016.08.011

M3 - Journal article

AN - SCOPUS:84994043937

SN - 0005-1098

VL - 75

SP - 11

EP - 15

JO - Automatica

JF - Automatica

ER -

Relaxed conditions for stability of time-varying delay systems

Abstract

Keywords

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