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Global stabilization of some chaotic dynamical systems

Author

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  • El-Dessoky, M.M.
  • Agiza, H.N.

Abstract

In this paper, based on the theory of nonlinear differential equations and Gerschgorin theorem, a control scheme is proposed for global stabilizing the unstable equilibria of a class of chaotic systems. Using a suitable designing to the feedback gain matrix which depends on a few algebraic inequalities, chaotic orbits are suppressed and dragged to the target (system’s equilibria). The proposed scheme is successfully applied to some typical chaotic systems with different types of nonlinearities, such as Rossler system, Nuclear Spin Generator system, and Four-scroll attractor. Numerical simulation results are presented to verify our control method.

Suggested Citation

  • El-Dessoky, M.M. & Agiza, H.N., 2009. "Global stabilization of some chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1584-1598.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1584-1598
    DOI: 10.1016/j.chaos.2009.03.028
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    References listed on IDEAS

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    1. Molaei, M.R. & Umut, Ömür, 2008. "Generalized synchronization of nuclear spin generator system," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 227-232.
    2. Liao, Xiaoxin & Yu, Pei, 2006. "Chaos control for the family of Rössler systems using feedback controllers," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 91-107.
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    Cited by:

    1. Yan, Donglin & Wang, Weiyu & Chen, Qijuan, 2018. "Fractional-order modeling and dynamic analyses of a bending-torsional coupling generator rotor shaft system with multiple faults," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 1-15.

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