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Novel Delay-Dependent Stabilization Criterion for Lur’e Systems with Sector-Restricted Nonlinearities and External Disturbances via PD Feedback Approach

Author

Listed:
  • Chun Yin

    (University of Electronic Science and Technology of China
    University of Electronic Science and Technology of China)

  • Shouming Zhong

    (University of Electronic Science and Technology of China
    University of Electronic Science and Technology of China)

  • Xiaoyun Liu

    (University of Electronic Science and Technology of China)

  • Zijian Liu

    (University of Electronic Science and Technology of China
    University of Electronic Science and Technology of China)

Abstract

In this paper, the effects of time delay on control of Lur’e systems are considered. Using a convex representation of the nonlinearity, a novel delay-dependent stability criterion is derived for the Lur’e systems via proportional-derivative (PD) feedback law. The Lyapunov–Krasovskii functional based on the delay discretization approach is used for the purpose of obtaining the stability condition by utilizing Projection Lemma. The criterion is utilized to not only guarantee stability of systems but also reduce the effect of external disturbance to an norm constraint. Finally, two numerical examples show the effectiveness of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:1:d:10.1007_s10957-011-9857-8
    DOI: 10.1007/s10957-011-9857-8
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    References listed on IDEAS

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    1. P. T. Nam & V. N. Phat, 2009. "Robust Stabilization of Linear Systems with Delayed State and Control," Journal of Optimization Theory and Applications, Springer, vol. 140(2), pages 287-299, February.
    2. J. H. Park, 2001. "Robust Stabilization for Dynamic Systems with Multiple Time-Varying Delays and Nonlinear Uncertainties," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 155-174, January.
    3. 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.
    4. M. S. Mahmoud & Y. Xia, 2009. "Robust Stability and Stabilization of a Class of Nonlinear Switched Discrete-Time Systems with Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 329-355, November.
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