IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3518-d926295.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3518/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3518/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sun, Meng & Zhuang, Guangming & Xia, Jianwei & Wang, Yanqian & Chen, Guoliang, 2022. "Stochastic admissibility and H∞ output feedback control for singular Markov jump systems under dynamic measurement output event-triggered strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Zhang, Xin & Shi, Ran, 2022. "Novel fast fixed-time sliding mode trajectory tracking control for manipulator," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    3. Amin Najafi & Mai The Vu & Saleh Mobayen & Jihad H. Asad & Afef Fekih, 2022. "Adaptive Barrier Fast Terminal Sliding Mode Actuator Fault Tolerant Control Approach for Quadrotor UAVs," Mathematics, MDPI, vol. 10(16), pages 1-22, August.
    4. 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.
    5. Yassine Bouteraa & Javad Mostafaee & Mourad Kchaou & Rabeh Abbassi & Houssem Jerbi & Saleh Mobayen, 2022. "A New Simple Chaotic System with One Nonlinear Term," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    6. Mousavi, Yashar & Bevan, Geraint & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Sliding mode control of wind energy conversion systems: Trends and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 167(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3518-:d:926295. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.