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Robust Analysis and Synthesis for the Nonexistence of Periodic Solutions in a Class of Nonlinear Systems

Author

Listed:
  • P. L. Lu

    (Peking University)

  • Y. Yang

    (Peking University)

  • L. Huang

    (Peking University)

Abstract

This paper considers the nonexistence of periodic solutions in a class of nonlinear uncertain systems. Based on the generalized Kalman–Yakubovich–Popov (GKYP) lemma, linear matrix inequalities (LMIs) characterizations are derived to guarantee the nonexistence of periodic solutions in a certain frequency range. The new LMI conditions do not involve any product of the Lyapunov matrix and the system matrices. Based on the results, a dynamic output feedback controller is designed to ensure the nonexistence of periodic solutions in such systems. A concrete application to the Chua circuit shows the applicability and validity of the proposed approach.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:2:d:10.1007_s10957-007-9241-x
    DOI: 10.1007/s10957-007-9241-x
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    Cited by:

    1. 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.

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