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Practical Synchronization Of Nonautonomous Systems With Uncertain Parameter Mismatch Via A Single State Feedback Control

Author

Listed:
  • MIHUA MA

    (Shanghai Institute of Applied Mathematics and Mechanics and Shanghai, Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China;
    Department of Mathematics, Zhangzhou Normal University, Zhangzhou 363000, P. R. China)

  • JIN ZHOU

    (Shanghai Institute of Applied Mathematics and Mechanics and Shanghai, Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China)

  • JIANPING CAI

    (Department of Mathematics, Zhangzhou Normal University, Zhangzhou 363000, P. R. China)

Abstract

Robust practical synchronization of general second-order nonautonomous systems with uncertain parameter mismatch is investigated by using a single state feedback control. Some simple general algebraic criteria are derived based on practical stability theory of nonautonomous dynamical system. A distinctive feature of this work is that the parameter mismatch not only exists in system parameters, but also in the external excitation ones. More reasonably, the values of parameter mismatch can be uncertain. Besides, a single state feedback control including an approximate differentiation filter only needs to know information about one state, which provides an advantage over the use of full-state model-based observers. It is shown that the approaches developed here further extend the ideas and techniques presented in recent literature. As a direct application of the new theoretical results, the obtained results are applied to a typical horizontal platform system and the representative forced Duffing–Van der Pol oscillator. Subsequently, numerical simulations demonstrate the effectiveness of the criteria and the robustness of the control technique.

Suggested Citation

  • Mihua Ma & Jin Zhou & Jianping Cai, 2012. "Practical Synchronization Of Nonautonomous Systems With Uncertain Parameter Mismatch Via A Single State Feedback Control," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 23(11), pages 1-14.
    • Handle: RePEc:wsi:ijmpcx:v:23:y:2012:i:11:n:s0129183112500738
    DOI: 10.1142/S0129183112500738
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