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A novel condition for fixed-time stability and its application in controller design for robust fixed-time chaos stabilization against Hölder continuous uncertainties

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Abstract

This paper presents a new nonlinear state-feedback controller design for robust fixed-time chaos stabilization of chaotic systems in the presence of a relatively large class of uncertainties known as Hölder continuous uncertainties. Based on Lyapunov's second method, a novel sufficient condition for fixed-time stability is derived. The spectacular property of the proposed controller is that the upper bound of the convergence time exists as an explicit parameter in the control's law, thus the true fixed stabilization time can be set in advance. To show the effectiveness of the proposed controller, two scenarios are provided, and the simulation results are reported.

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Shahid Beheshti University, P.O. Box 1658953571, Tehran, Iran

    Alireza Khanzadeh & Mahdi Pourgholi

  2. Department of Electrical and Computer Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran

    Elham Amini Boroujeni

Authors
  1. Alireza Khanzadeh
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  2. Mahdi Pourgholi
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  3. Elham Amini Boroujeni
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Corresponding author

Correspondence to Mahdi Pourgholi.

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Communicated by V. Loia.

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Khanzadeh, A., Pourgholi, M. & Amini Boroujeni, E. A novel condition for fixed-time stability and its application in controller design for robust fixed-time chaos stabilization against Hölder continuous uncertainties. Soft Comput 25, 3903–3911 (2021). https://doi.org/10.1007/s00500-020-05415-4

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  • DOI: https://doi.org/10.1007/s00500-020-05415-4

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