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Synchronization of chaotic fractional-order systems via active sliding mode controller

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  • Tavazoei, Mohammad Saleh
  • Haeri, Mohammad

Abstract

In this paper, we propose a controller based on active sliding mode theory to synchronize chaotic fractional-order systems in master–slave structure. Master and slave systems may be identical or different. Based on stability theorems in the fractional calculus, analysis of stability is performed for the proposed method. Finally, three numerical simulations (synchronizing fractional-order Lü–Lü systems, synchronizing fractional order Chen–Chen systems and synchronizing fractional-order Lü–Chen systems) are presented to show the effectiveness of the proposed controller. The simulations are implemented using two different numerical methods to solve the fractional differential equations.

Suggested Citation

  • Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2008. "Synchronization of chaotic fractional-order systems via active sliding mode controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 57-70.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:1:p:57-70
    DOI: 10.1016/j.physa.2007.08.039
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    References listed on IDEAS

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    Cited by:

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    12. Khanzadeh, Alireza & Pourgholi, Mahdi, 2016. "Robust Synchronization of Fractional-Order Chaotic Systems at a Pre-Specified Time Using Sliding Mode Controller with Time-Varying Switching Surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 69-77.
    13. Gao, Yuan & Liang, Chenghua & Wu, Qiqi & Yuan, Haiying, 2015. "A new fractional-order hyperchaotic system and its modified projective synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 190-204.
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