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LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation

Author

Listed:
  • Hamede Karami

    (Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran)

  • Saleh Mobayen

    (Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran
    Future Technology Research Center, National Yunlin University of Science and Technology, Yunlin 64002, Taiwan)

  • Marzieh Lashkari

    (Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran)

  • Farhad Bayat

    (Department of Electrical Engineering, University of Zanjan, Zanjan 45371-38791, Iran)

  • Arthur Chang

    (Bachelor Program in Interdisciplinary Studies, National Yunlin University of Science and Technology, Yunlin 64002, Taiwan)

Abstract

In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches.

Suggested Citation

  • Hamede Karami & Saleh Mobayen & Marzieh Lashkari & Farhad Bayat & Arthur Chang, 2021. "LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1128-:d:555715
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    References listed on IDEAS

    as
    1. Park, Ju H., 2005. "Controlling chaotic systems via nonlinear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 1049-1054.
    2. Ma, Yutian & Li, Wenwen, 2020. "Application and research of fractional differential equations in dynamic analysis of supply chain financial chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Hassène Gritli & Ali Zemouche & Safya Belghith, 2021. "On LMI conditions to design robust static output feedback controller for continuous-time linear systems subject to norm-bounded uncertainties," International Journal of Systems Science, Taylor & Francis Journals, vol. 52(1), pages 12-46, January.
    4. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
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    Cited by:

    1. Masoud Chatavi & Mai The Vu & Saleh Mobayen & Afef Fekih, 2022. "H ∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances," Mathematics, MDPI, vol. 10(19), pages 1-19, September.

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