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LMI-based stabilization of a class of fractional-order chaotic systems

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Abstract

Based on the theory of stabilization of fractional-order LTI interval systems, a simple controller for stabilization of a class of fractional-order chaotic systems is proposed in this paper. We consider the structure of the chaotic systems as fractional-order LTI interval systems due to the limited amplitude of chaotic trajectories. We introduce a simple feedback controller for the interval system and then, based on a recently established theorem for stabilization of interval systems, we reach to a linear matrix inequality (LMI) problem. Solving the LMI yields an appropriate decoupling feedback control law which suffices to bring the chaotic trajectories to the origin. Several illustrative examples are given which show the effectiveness of the method.

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Authors and Affiliations

  1. Department of Electrical Engineering, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran

    Mohammadreza Faieghi

  2. Department of Mechanical and Aerospace Engineering, Faculty of Engineering, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Suwat Kuntanapreeda

  3. Department of Electrical Engineering, Hamedan University of Technology, Hamedan, 65155, Iran

    Hadi Delavari

  4. Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  5. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Baleanu

Authors
  1. Mohammadreza Faieghi
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  2. Suwat Kuntanapreeda
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  3. Hadi Delavari
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  4. Dumitru Baleanu
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Corresponding author

Correspondence to Hadi Delavari.

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Faieghi, M., Kuntanapreeda, S., Delavari, H. et al. LMI-based stabilization of a class of fractional-order chaotic systems. Nonlinear Dyn 72, 301–309 (2013). https://doi.org/10.1007/s11071-012-0714-6

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  • DOI: https://doi.org/10.1007/s11071-012-0714-6

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