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H ∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances

Author

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  • Masoud Chatavi

    (Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15875, Iran
    Masoud Chatavi and Mai The Vu are the first authors; these authors contributed equally to this work.)

  • Mai The Vu

    (School of Intelligent Mechatronics Engineering, Sejong University, Seoul 05006, Korea
    Masoud Chatavi and Mai The Vu are the first authors; these authors contributed equally to this work.)

  • Saleh Mobayen

    (Future Technology Research Center, National Yunlin University of Science and Technology, Douliou, Yunlin 64002, Taiwan)

  • Afef Fekih

    (Department of Electrical and Computer Engineering, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

Abstract

In this paper, we propose a nonlinear state feedback controller based on linear matrix inequality (LMI) for a class of nonlinear systems with parametric uncertainties and external disturbances. The primary goals of the proposed controller are to guarantee system stability and performance in the presence of system uncertainties and time-dependent disturbances. To meet the specified objectives, the LMI form is calculated as a hierarchical control structure. Using the Lyapunov stability function, the asymptotic stability of the nominal system obtained from the nonlinear state feedback is proven, and the LMI condition is attained. After applying the nonlinear state feedback controller, asymptotic stability conditions for the nominal system are constructed using the Lyapunov function, and the nonlinear state-feedback control mechanism is determined accordingly. Considering the external disturbance as input, the terms of the state matrices are substituted in the obtained LMI, and the LMI condition for a nominal system is achieved in the presence of disturbances. The asymptotic stability condition of the uncertain system in the presence of external disturbances is determined by adding uncertainties to the system. The proposed approach yields a simple control mechanism representing an independent of system order. The performance of the proposed approach was assessed using a simulation study of a ball and beam system.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3518-:d:926295
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Mobayen, Saleh & Alattas, Khalid A. & Fekih, Afef & El-Sousy, Fayez F.M. & Bakouri, Mohsen, 2022. "Barrier function-based adaptive nonsingular sliding mode control of disturbed nonlinear systems: A linear matrix inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Kamran Naseri & Mai The Vu & Saleh Mobayen & Amin Najafi & Afef Fekih, 2022. "Design of Linear Matrix Inequality-Based Adaptive Barrier Global Sliding Mode Fault Tolerant Control for Uncertain Systems with Faulty Actuators," Mathematics, MDPI, vol. 10(13), pages 1-14, June.
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