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Chaos control for the family of Rössler systems using feedback controllers

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  • Liao, Xiaoxin
  • Yu, Pei

Abstract

This paper presents a new method for controlling chaos in several classical chaotic Rössler systems using feedback control strategy. In particular, for an arbitrarily given equilibrium point of a Rössler system, we design explicit and simple feedback control laws by which the equilibrium point is globally and exponentially stabilized. Six typical Rössler systems are studied, and explicit formulas are derived for estimating the convergence rate of these systems. Numerical examples are presented to illustrate the theoretical results. A mistake has been found in the existing literature, and a correct result is given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:29:y:2006:i:1:p:91-107
    DOI: 10.1016/j.chaos.2004.12.046
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    Cited by:

    1. 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.
    2. Liao, Xiaoxin & Xu, F. & Wang, P. & Yu, Pei, 2009. "Chaos control and synchronization for a special generalized Lorenz canonical system – The SM system," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2491-2508.
    3. Falahpoor, M. & Ataei, M. & Kiyoumarsi, A., 2009. "A chattering-free sliding mode control design for uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1755-1765.

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