Synchronization Criterion for Lur'e Systems via Delayed PD Controller

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

doi:10.1007/s10957-010-9723-0

Synchronization Criterion for Lur'e Systems via Delayed PD Controller

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

School of Electronics Engineering

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

18 Scopus citations

Abstract

In this paper, the effects of a time varying delay on a chaotic drive-response synchronization are considered. Using a delayed feedback proportional-derivative (PD) controller scheme, a delay-dependent synchronization criterion is derived for chaotic systems represented by the Lur'e system with sector and slope restricted nonlinearities. The derived criterion is a sufficient condition for the absolute stability of the error dynamics between the drive and the response systems. By the use of a convex representation of the nonlinearity and the discretized Lyapunov-Krasovskii functional, stability condition is obtained via the LMI formulation. The condition represented in the terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.

Original language	English
Pages (from-to)	298-317
Number of pages	20
Journal	Journal of Optimization Theory and Applications
Volume	147
Issue number	2
DOIs	https://doi.org/10.1007/s10957-010-9723-0
State	Published - 2010

Keywords

Absolute stability
Convex optimization
LMIs
Lur'e systems
PD controller
Synchronization

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10.1007/s10957-010-9723-0

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title = "Synchronization Criterion for Lur'e Systems via Delayed PD Controller",

abstract = "In this paper, the effects of a time varying delay on a chaotic drive-response synchronization are considered. Using a delayed feedback proportional-derivative (PD) controller scheme, a delay-dependent synchronization criterion is derived for chaotic systems represented by the Lur'e system with sector and slope restricted nonlinearities. The derived criterion is a sufficient condition for the absolute stability of the error dynamics between the drive and the response systems. By the use of a convex representation of the nonlinearity and the discretized Lyapunov-Krasovskii functional, stability condition is obtained via the LMI formulation. The condition represented in the terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.",

keywords = "Absolute stability, Convex optimization, LMIs, Lur'e systems, PD controller, Synchronization",

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T1 - Synchronization Criterion for Lur'e Systems via Delayed PD Controller

AU - Ji, D. H.

AU - Park, Ju H.

AU - Lee, S. M.

AU - Koo, J. H.

AU - Won, S. C.

PY - 2010

Y1 - 2010

N2 - In this paper, the effects of a time varying delay on a chaotic drive-response synchronization are considered. Using a delayed feedback proportional-derivative (PD) controller scheme, a delay-dependent synchronization criterion is derived for chaotic systems represented by the Lur'e system with sector and slope restricted nonlinearities. The derived criterion is a sufficient condition for the absolute stability of the error dynamics between the drive and the response systems. By the use of a convex representation of the nonlinearity and the discretized Lyapunov-Krasovskii functional, stability condition is obtained via the LMI formulation. The condition represented in the terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.

AB - In this paper, the effects of a time varying delay on a chaotic drive-response synchronization are considered. Using a delayed feedback proportional-derivative (PD) controller scheme, a delay-dependent synchronization criterion is derived for chaotic systems represented by the Lur'e system with sector and slope restricted nonlinearities. The derived criterion is a sufficient condition for the absolute stability of the error dynamics between the drive and the response systems. By the use of a convex representation of the nonlinearity and the discretized Lyapunov-Krasovskii functional, stability condition is obtained via the LMI formulation. The condition represented in the terms of linear matrix inequalities (LMIs) can be solved by the application of convex optimization algorithms. The effectiveness of the work is verified through numerical examples.

KW - Absolute stability

KW - Convex optimization

KW - LMIs

KW - Lur'e systems

KW - PD controller

KW - Synchronization

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JO - Journal of Optimization Theory and Applications

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Synchronization Criterion for Lur'e Systems via Delayed PD Controller

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