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Parametric Controller Design of Hopf Bifurcation System

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  • Jinbo Lu
  • Xiaorong Hou
  • Min Luo

Abstract

A general parametric controller design method is proposed for Hopf bifurcation of nonlinear dynamic system. This method does not increase the dimension of the system. Compared with the existing methods, the controller designed by this method has a lower controller order and a simpler structure, and it does not contain equilibrium points. The method keeps equilibrium of the origin system unchanged. Symbolic computation is used to deduce the constraints of controller, and cylindrical algebraic decomposition is used to find the stability parameter regions in parameter space of controller. The method is then employed for Hopf bifurcation control. Taking Lorenz system as an example, the controller design steps of the method and numerical simulations are discussed. Computer simulation results are presented to confirm the analytical predictions.

Suggested Citation

  • Jinbo Lu & Xiaorong Hou & Min Luo, 2015. "Parametric Controller Design of Hopf Bifurcation System," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, December.
    • Handle: RePEc:hin:jnlmpe:584954
    DOI: 10.1155/2015/584954
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    Cited by:

    1. Yang, Jing & Hou, Xiaorong & Li, Xiaoxue & Luo, Min, 2022. "A parameter space method for analyzing Hopf bifurcation of fractional-order nonlinear systems with multiple-parameter," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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