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Robust global fixed-time synchronization of different dimensions fractional-order chaotic systems

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  • Shirkavand, Mehrdad
  • Pourgholi, Mahdi
  • Yazdizadeh, Alireza

Abstract

This paper addresses the problem of global fixed-time synchronization of two fractional chaotic systems with different dimensions in the presence of matched bounded and differentiable exogenous disturbances and uncertainties in the systems. Firstly, a novel fixed-time stable dynamical system is investigated wherein the upper bound estimate of the settling time of synchronization is determined by a priori value dependent on a design parameter regardless of the initial conditions. The introduced dynamical system to guarantee fixed-time stability is completely different from that in the existing works of literature. Based on the introduced fixed-time dynamic, a novel controller is designed that guarantees globally synchronization of two fractional chaotic systems with different dimensions within the fixed-time. Afterward, the result of synchronization of two different dimensional fractional chaotic systems within the fixed-time is extended to the networked ones. Finally, the effectiveness and validity of the results of the theoretical analysis are demonstrated by the illustrative examples and their numerical simulations.

Suggested Citation

  • Shirkavand, Mehrdad & Pourgholi, Mahdi & Yazdizadeh, Alireza, 2022. "Robust global fixed-time synchronization of different dimensions fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:chsofr:v:154:y:2022:i:c:s096007792100970x
    DOI: 10.1016/j.chaos.2021.111616
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    1. Alsaade, Fawaz W. & Yao, Qijia & Bekiros, Stelios & Al-zahrani, Mohammed S. & Alzahrani, Ali S. & Jahanshahi, Hadi, 2022. "Chaotic attitude synchronization and anti-synchronization of master-slave satellites using a robust fixed-time adaptive controller," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    2. Yao, Qijia & Alsaade, Fawaz W. & Al-zahrani, Mohammed S. & Jahanshahi, Hadi, 2023. "Fixed-time neural control for output-constrained synchronization of second-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    3. Luo, Runzi & Liu, Shuai & Song, Zijun & Zhang, Fang, 2023. "Fixed-time control of a class of fractional-order chaotic systems via backstepping method," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    4. Luo, Runzi & Song, Zijun & Liu, Shuai, 2023. "Fixed-time observed synchronization of chaotic system with all state variables unavailable in some periods," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

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