Further improvement of free-weighting matrices technique for systems with time-varying delay

Yong He; Qing Gao Wang; Lihua Xie; Chong Lin

doi:10.1109/TAC.2006.887907

Further improvement of free-weighting matrices technique for systems with time-varying delay

Yong He, Qing Gao Wang, Lihua Xie, Chong Lin

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

762 Citations (Scopus)

Abstract

A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

Original language	English
Pages (from-to)	293-299
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	52
Issue number	2
DOIs	https://doi.org/10.1109/TAC.2006.887907
Publication status	Published - Feb 2007
Externally published	Yes

Keywords

Augmented Lyapunov functional
Delay-dependent
Linear matrix inequality (LMI)
Stability
Time-varying delay

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2006.887907

Cite this

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title = "Further improvement of free-weighting matrices technique for systems with time-varying delay",

abstract = "A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.",

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author = "Yong He and Wang, {Qing Gao} and Lihua Xie and Chong Lin",

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AU - He, Yong

AU - Wang, Qing Gao

AU - Xie, Lihua

AU - Lin, Chong

PY - 2007/2

Y1 - 2007/2

N2 - A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

AB - A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

KW - Augmented Lyapunov functional

KW - Delay-dependent

KW - Linear matrix inequality (LMI)

KW - Stability

KW - Time-varying delay

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JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

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ER -

Further improvement of free-weighting matrices technique for systems with time-varying delay

Abstract

Keywords

ASJC Scopus subject areas

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