New conditions for delay-derivative-dependent stability

Emilia Fridman; Uri Shaked; Kun Liu

doi:10.1016/j.automatica.2009.08.002

New conditions for delay-derivative-dependent stability

Emilia Fridman^*, Uri Shaked, Kun Liu

^*Corresponding author for this work

Tel Aviv University

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

186 Citations (Scopus)

Abstract

Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov-Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.

Original language	English
Pages (from-to)	2723-2727
Number of pages	5
Journal	Automatica
Volume	45
Issue number	11
DOIs	https://doi.org/10.1016/j.automatica.2009.08.002
Publication status	Published - Nov 2009
Externally published	Yes

Keywords

LMI
Lyapunov-Krasovskii functional
Time-varying delay

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10.1016/j.automatica.2009.08.002

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Fridman, E., Shaked, U., & Liu, K. (2009). New conditions for delay-derivative-dependent stability. Automatica, 45(11), 2723-2727. https://doi.org/10.1016/j.automatica.2009.08.002

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abstract = "Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov-Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.",

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AU - Fridman, Emilia

AU - Shaked, Uri

AU - Liu, Kun

PY - 2009/11

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N2 - Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov-Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.

AB - Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov-Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.

KW - LMI

KW - Lyapunov-Krasovskii functional

KW - Time-varying delay

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DO - 10.1016/j.automatica.2009.08.002

M3 - Article

AN - SCOPUS:70349850642

SN - 0005-1098

VL - 45

SP - 2723

EP - 2727

JO - Automatica

JF - Automatica

IS - 11

ER -

New conditions for delay-derivative-dependent stability

Abstract

Keywords

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