Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay

D. H. Ji; Ju H. Park; W. J. Yoo; S. C. Won; S. M. Lee

doi:10.1016/j.physleta.2010.01.005

Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay

D. H. Ji, Ju H. Park, W. J. Yoo, S. C. Won, S. M. Lee

School of Electronics Engineering

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

67 Scopus citations

Abstract

In this Letter, the synchronization problem for a class of complex dynamical networks in which every identical node is a Lur'e system with time-varying delay is considered. A delay-dependent synchronization criterion is derived for the synchronization of complex dynamical network that represented by Lur'e system with sector restricted nonlinearities. The derived criterion is a sufficient condition for absolute stability of error dynamics between the each nodes and the isolated node. Using a convex representation of the nonlinearity for error dynamics, the stability condition based on the discretized Lyapunov-Krasovskii functional is obtained via LMI formulation. The proposed delay-dependent synchronization criterion is less conservative than the existing ones. The effectiveness of our work is verified through numerical examples.

Original language	English
Pages (from-to)	1218-1227
Number of pages	10
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	374
Issue number	10
DOIs	https://doi.org/10.1016/j.physleta.2010.01.005
State	Published - 22 Feb 2010

Keywords

Absolute stability
Complex dynamical networks
Delay dependent criterion
LMIs
Lur'e systems
Synchronization

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10.1016/j.physleta.2010.01.005

Cite this

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abstract = "In this Letter, the synchronization problem for a class of complex dynamical networks in which every identical node is a Lur'e system with time-varying delay is considered. A delay-dependent synchronization criterion is derived for the synchronization of complex dynamical network that represented by Lur'e system with sector restricted nonlinearities. The derived criterion is a sufficient condition for absolute stability of error dynamics between the each nodes and the isolated node. Using a convex representation of the nonlinearity for error dynamics, the stability condition based on the discretized Lyapunov-Krasovskii functional is obtained via LMI formulation. The proposed delay-dependent synchronization criterion is less conservative than the existing ones. The effectiveness of our work is verified through numerical examples.",

keywords = "Absolute stability, Complex dynamical networks, Delay dependent criterion, LMIs, Lur'e systems, Synchronization",

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AU - Ji, D. H.

AU - Park, Ju H.

AU - Yoo, W. J.

AU - Won, S. C.

AU - Lee, S. M.

PY - 2010/2/22

Y1 - 2010/2/22

N2 - In this Letter, the synchronization problem for a class of complex dynamical networks in which every identical node is a Lur'e system with time-varying delay is considered. A delay-dependent synchronization criterion is derived for the synchronization of complex dynamical network that represented by Lur'e system with sector restricted nonlinearities. The derived criterion is a sufficient condition for absolute stability of error dynamics between the each nodes and the isolated node. Using a convex representation of the nonlinearity for error dynamics, the stability condition based on the discretized Lyapunov-Krasovskii functional is obtained via LMI formulation. The proposed delay-dependent synchronization criterion is less conservative than the existing ones. The effectiveness of our work is verified through numerical examples.

AB - In this Letter, the synchronization problem for a class of complex dynamical networks in which every identical node is a Lur'e system with time-varying delay is considered. A delay-dependent synchronization criterion is derived for the synchronization of complex dynamical network that represented by Lur'e system with sector restricted nonlinearities. The derived criterion is a sufficient condition for absolute stability of error dynamics between the each nodes and the isolated node. Using a convex representation of the nonlinearity for error dynamics, the stability condition based on the discretized Lyapunov-Krasovskii functional is obtained via LMI formulation. The proposed delay-dependent synchronization criterion is less conservative than the existing ones. The effectiveness of our work is verified through numerical examples.

KW - Absolute stability

KW - Complex dynamical networks

KW - Delay dependent criterion

KW - LMIs

KW - Lur'e systems

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Synchronization criterion for Lur'e type complex dynamical networks with time-varying delay

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Keywords

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