IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3438-d921447.html
   My bibliography  Save this article

Local H ∞ Control for Continuous-Time T-S Fuzzy Systems via Generalized Non-Quadratic Lyapunov Functions

Author

Listed:
  • Guolin Hu

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Jian Zhang

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Zhiguo Yan

    (School of Information and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

Abstract

This paper further develops a relaxed method to reduce conservatism in H ∞ feedback control for continuous-time T-S fuzzy systems via a generalized non-quadratic Lyapunov function. Different from the results of some exisiting works, the generalized H ∞ state feedback controller is designed. The relaxed stabilization conditions are obtained by applying Finsler’s lemma with the homogenous polynomial multipliers, and the H ∞ performance is acquired by solving an optimization problem. In addition, the proposed method could be expanded to handle other control problems for fuzzy systems. Two examples are given to show the validity of the proposed results.

Suggested Citation

  • Guolin Hu & Jian Zhang & Zhiguo Yan, 2022. "Local H ∞ Control for Continuous-Time T-S Fuzzy Systems via Generalized Non-Quadratic Lyapunov Functions," Mathematics, MDPI, vol. 10(19), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3438-:d:921447
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3438/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3438/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Flávio Faria & Geraldo Silva & Vilma Oliveira, 2013. "Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(10), pages 1956-1969.
    2. Xiao-Heng Chang & Guang-Hong Yang & Haibo Wang, 2011. "Observer-based -control for discrete-time T–S fuzzy systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(10), pages 1801-1809.
    3. Hakim Achour & Djamel Boukhetala & Hilal Labdelaoui, 2020. "An observer-based robust H∞ controller design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using particle swarm optimisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(14), pages 2563-2581, October.
    4. Yan, Zhiguo & Zhang, Min & Chang, Gaizhen & Lv, Hui & Park, Ju H., 2022. "Finite-time annular domain stability and stabilization of Itô stochastic systems with Wiener noise and Poisson jumps-differential Gronwall inequality approach," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    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. Zhiguo Yan & Zhiwei Zhang & Guolin Hu & Baolong Zhu, 2022. "Observer-Based Finite-Time H ∞ Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model," Mathematics, MDPI, vol. 10(12), pages 1-15, June.
    2. Mohammad Hassan Asemani & Vahid Johari Majd, 2015. "A robust -tracking design for uncertain Takagi–Sugeno fuzzy systems with unknown premise variables using descriptor redundancy approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(16), pages 2955-2972, December.
    3. Thanh Binh Nguyen & Hyoung-Kyu Song, 2022. "Further Results on Robust Output-Feedback Dissipative Control of Markovian Jump Fuzzy Systems with Model Uncertainties," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    4. R. Rakkiyappan & A. Chandrasekar & S. Lakshmanan, 2016. "Stochastic sampled data robust stabilisation of T-S fuzzy neutral systems with randomly occurring uncertainties and time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(10), pages 2247-2263, July.

    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:3438-:d:921447. 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.