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Synchronization Criterion for Lur’e Systems via Delayed PD Controller

Author

Listed:
  • D. H. Ji

    (Samsung Electronics)

  • Ju H. Park

    (Yeungnam University)

  • S. M. Lee

    (Daegu University)

  • J. H. Koo

    (POSTECH)

  • S. C. Won

    (POSTECH)

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.

Suggested Citation

  • D. H. Ji & Ju H. Park & S. M. Lee & J. H. Koo & S. C. Won, 2010. "Synchronization Criterion for Lur’e Systems via Delayed PD Controller," Journal of Optimization Theory and Applications, Springer, vol. 147(2), pages 298-317, November.
    • Handle: RePEc:spr:joptap:v:147:y:2010:i:2:d:10.1007_s10957-010-9723-0
    DOI: 10.1007/s10957-010-9723-0
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    References listed on IDEAS

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    1. J. H. Park & S. Won, 1999. "Asymptotic Stability of Neutral Systems with Multiple Delays," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 183-200, October.
    2. Wen, Guilin & Wang, Qing-Guo & Lin, Chong & Han, Xu & Li, Guangyao, 2006. "Synthesis for robust synchronization of chaotic systems under output feedback control with multiple random delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1142-1146.
    3. Cao, Jinde & Li, H.X. & Ho, Daniel W.C., 2005. "Synchronization criteria of Lur’e systems with time-delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1285-1298.
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    Cited by:

    1. Chun Yin & Shouming Zhong & Xiaoyun Liu & Zijian Liu, 2011. "Novel Delay-Dependent Stabilization Criterion for Lur’e Systems with Sector-Restricted Nonlinearities and External Disturbances via PD Feedback Approach," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 81-99, October.

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