Stability analysis for linear time-delay systems using new inequality based on the second-order derivative

Xin Zhao; Chong Lin; Bing Chen; Qing Guo Wang

doi:10.1016/j.jfranklin.2019.03.038

Stability analysis for linear time-delay systems using new inequality based on the second-order derivative

Xin Zhao
, Chong Lin
, Bing Chen
, Qing Guo Wang

Electrical and Electronic Engineering Science

Qingdao University

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

This paper studies the stability problem of linear time-varying delay system. Firstly, a double integral inequality based on the second-order derivative is proposed in this paper. Secondly, novel Lyapunov–Krasovskii functional consisting of integral terms based on the second-order derivative is constructed to enhance the feasible region of delay-dependent stability. Based on the two aspects, new delay-dependent stability criteria which guarantee the asymptotic stability of linear systems with time-varying delay are given in the form of linear matrix inequality (LMI). Finally, several numerical examples are given to show the advantages of the proposed methods.

Original language	English
Pages (from-to)	8770-8784
Number of pages	15
Journal	Journal of the Franklin Institute
Volume	356
Issue number	15
DOIs	https://doi.org/10.1016/j.jfranklin.2019.03.038
Publication status	Published - Oct 2019

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

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10.1016/j.jfranklin.2019.03.038

Cite this

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title = "Stability analysis for linear time-delay systems using new inequality based on the second-order derivative",

abstract = "This paper studies the stability problem of linear time-varying delay system. Firstly, a double integral inequality based on the second-order derivative is proposed in this paper. Secondly, novel Lyapunov–Krasovskii functional consisting of integral terms based on the second-order derivative is constructed to enhance the feasible region of delay-dependent stability. Based on the two aspects, new delay-dependent stability criteria which guarantee the asymptotic stability of linear systems with time-varying delay are given in the form of linear matrix inequality (LMI). Finally, several numerical examples are given to show the advantages of the proposed methods.",

author = "Xin Zhao and Chong Lin and Bing Chen and Wang, \{Qing Guo\}",

note = "Publisher Copyright: {\textcopyright} 2019 The Franklin Institute",

year = "2019",

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AU - Zhao, Xin

AU - Lin, Chong

AU - Chen, Bing

AU - Wang, Qing Guo

PY - 2019/10

Y1 - 2019/10

N2 - This paper studies the stability problem of linear time-varying delay system. Firstly, a double integral inequality based on the second-order derivative is proposed in this paper. Secondly, novel Lyapunov–Krasovskii functional consisting of integral terms based on the second-order derivative is constructed to enhance the feasible region of delay-dependent stability. Based on the two aspects, new delay-dependent stability criteria which guarantee the asymptotic stability of linear systems with time-varying delay are given in the form of linear matrix inequality (LMI). Finally, several numerical examples are given to show the advantages of the proposed methods.

AB - This paper studies the stability problem of linear time-varying delay system. Firstly, a double integral inequality based on the second-order derivative is proposed in this paper. Secondly, novel Lyapunov–Krasovskii functional consisting of integral terms based on the second-order derivative is constructed to enhance the feasible region of delay-dependent stability. Based on the two aspects, new delay-dependent stability criteria which guarantee the asymptotic stability of linear systems with time-varying delay are given in the form of linear matrix inequality (LMI). Finally, several numerical examples are given to show the advantages of the proposed methods.

UR - https://www.scopus.com/pages/publications/85072090489

U2 - 10.1016/j.jfranklin.2019.03.038

DO - 10.1016/j.jfranklin.2019.03.038

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VL - 356

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EP - 8784

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 15

ER -

Stability analysis for linear time-delay systems using new inequality based on the second-order derivative

Abstract

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