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Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability

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  • Chunlai Li
  • Jing Zhang

Abstract

The issue of synchronisation for a fractional-order chaotic system with uncertainties and disturbance is studied in this paper. The finite-time input-to-state stable theory of fractional-order dynamical system is presented for the first time. A linear feedback controller is proposed to achieve synchronisation of this fractional-order system and guarantee the bounded state error for any bounded interference in finite time. Since the chaotic system displays special dynamical behaviours as invariable Lyapunov exponent spectrums and controllable signal amplitude, one can achieve complete synchronisation and projective synchronisation by only adjusting the system parameter. Numerical simulations are shown to verify the feasibility of the presented synchronisation scheme.

Suggested Citation

  • Chunlai Li & Jing Zhang, 2016. "Synchronisation of a fractional-order chaotic system using finite-time input-to-state stability," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2440-2448, July.
    • Handle: RePEc:taf:tsysxx:v:47:y:2016:i:10:p:2440-2448
    DOI: 10.1080/00207721.2014.998741
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    1. Ge, Zheng-Ming & Jhuang, Wei-Ren, 2007. "Chaos, control and synchronization of a fractional order rotational mechanical system with a centrifugal governor," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 270-289.
    2. Lu, Jun Guo, 2006. "Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 107-118.
    3. Lu, Jun Guo, 2006. "Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 519-525.
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