Stability analysis of systems with time-varying delays via the second-order Bessel–Legendre inequality

Kun Liu; Alexandre Seuret; Yuanqing Xia

doi:10.1016/j.automatica.2016.11.001

Stability analysis of systems with time-varying delays via the second-order Bessel–Legendre inequality

Kun Liu, Alexandre Seuret, Yuanqing Xia

School of Automation

Université Fédérale Toulouse Midi-Pyrénées

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

242 Citations (Scopus)

Abstract

This paper is concerned with the delay-dependent stability of systems with time-varying delays. The novelty relies on the use of the second-order Bessel–Legendre integral inequality which is less conservative than the Jensen and Wirtinger-based inequalities. Unlike similar contributions, the features of this inequality are fully integrated into the construction of augmented Lyapunov–Krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities. The stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method.

Original language	English
Pages (from-to)	138-142
Number of pages	5
Journal	Automatica
Volume	76
DOIs	https://doi.org/10.1016/j.automatica.2016.11.001
Publication status	Published - 1 Feb 2017

Keywords

Integral inequality
Lyapunov method
Time-varying delays

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10.1016/j.automatica.2016.11.001

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abstract = "This paper is concerned with the delay-dependent stability of systems with time-varying delays. The novelty relies on the use of the second-order Bessel–Legendre integral inequality which is less conservative than the Jensen and Wirtinger-based inequalities. Unlike similar contributions, the features of this inequality are fully integrated into the construction of augmented Lyapunov–Krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities. The stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method.",

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N2 - This paper is concerned with the delay-dependent stability of systems with time-varying delays. The novelty relies on the use of the second-order Bessel–Legendre integral inequality which is less conservative than the Jensen and Wirtinger-based inequalities. Unlike similar contributions, the features of this inequality are fully integrated into the construction of augmented Lyapunov–Krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities. The stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method.

AB - This paper is concerned with the delay-dependent stability of systems with time-varying delays. The novelty relies on the use of the second-order Bessel–Legendre integral inequality which is less conservative than the Jensen and Wirtinger-based inequalities. Unlike similar contributions, the features of this inequality are fully integrated into the construction of augmented Lyapunov–Krasovskii functionals leading to novel stability criteria expressed in terms of linear matrix inequalities. The stability condition is tested on some classical numerical examples illustrating the efficiency of the proposed method.

KW - Integral inequality

KW - Lyapunov method

KW - Time-varying delays

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JO - Automatica

JF - Automatica

ER -

Stability analysis of systems with time-varying delays via the second-order Bessel–Legendre inequality

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Keywords

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