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Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria

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  • S. Y. Xu

    (Peking University)

  • Y. Yang

    (Peking University)

Abstract

This study concerns with the robust H ∞ synchronization problem for a class of nonlinear feedback control systems, which are subject to a vector-valued periodic nonlinearity in the feedback path. Under such synchronization configuration, the master system is assumed to be subject to an energy bounded input disturbance, and the slave one is under control. Sufficient conditions for controller design are proposed in terms of linear matrix inequalities by respectively utilizing the output feedback control and the dynamic output control strategies, such that the master system robustly synchronizes the slave one with a guaranteed H ∞ performance. The derived methods can be applied to the robust H ∞ synchronization of many practical systems, and effectiveness of the obtained results are demonstrated through a concrete example of phase-locked loops (PLL).

Suggested Citation

  • S. Y. Xu & Y. Yang, 2010. "Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria," Journal of Optimization Theory and Applications, Springer, vol. 146(3), pages 745-763, September.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:3:d:10.1007_s10957-010-9689-y
    DOI: 10.1007/s10957-010-9689-y
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    References listed on IDEAS

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    1. P. L. Lu & Y. Yang & L. Huang, 2007. "Robust Analysis and Synthesis for the Nonexistence of Periodic Solutions in a Class of Nonlinear Systems," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 205-216, November.
    2. Liu, Xian & Wang, Jinzhi & Huang, Lin, 2007. "Global synchronization for a class of dynamical complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 543-556.
    3. Sun, Jitao & Zhang, Yinping, 2004. "Impulsive control and synchronization of Chua’s oscillators," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(6), pages 499-508.
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