IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i17p2721-d1468345.html
   My bibliography  Save this article

Analysis and Controller Design for Parameter Varying T-S Fuzzy Systems with Markov Jump

Author

Listed:
  • Na Min

    (School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China)

  • Hongyang Zhang

    (School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510641, China)

Abstract

In this paper, we investigate a novel T-S fuzzy parameter varying system with Markov jump, in which parameters depend not only on a Markov chain but also on linear parameter varying elements that take values in convex polytopic sets. Stable conditions and the gain-scheduling controller design method for this system are obtained. Applying Lyapunov function depending on the operation mode and full block S-procedure lemma, we obtain stochastic stabilization conditions. We find that this novel system has two distinct advantages. On the one hand, it inherits the advantages of traditional T-S fuzzy systems in handling nonlinear objects under the frame of T-S fuzzy systems; on the other, it obtains the advantages of dealing with time-varying characteristics from the point of linear parameter varying (LPV) systems. Finally, the theory results are illustrated via numerical simulation.

Suggested Citation

  • Na Min & Hongyang Zhang, 2024. "Analysis and Controller Design for Parameter Varying T-S Fuzzy Systems with Markov Jump," Mathematics, MDPI, vol. 12(17), pages 1-19, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2721-:d:1468345
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/17/2721/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/17/2721/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Zhen & Wang, Jian, 2020. "Reachable set estimation for Markov jump LPV systems with time delays," Applied Mathematics and Computation, Elsevier, vol. 376(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. Liu, Yu-An & Tang, Shengdao & Liu, Yufan & Kong, Qingkai & Wang, Jing, 2021. "Extended dissipative sliding mode control for nonlinear networked control systems via event-triggered mechanism with random uncertain measurement," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Li, Xiaoqing & Nguang, Sing Kiong & She, Kun & Cheng, Jun & Zhong, Shouming, 2021. "Resilient controller synthesis for Markovian jump systems with probabilistic faults and gain fluctuations under stochastic sampling operational mechanism," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. Wu, Tianyu & Huang, Xia & Chen, Xiangyong & Wang, Jing, 2020. "Sampled-data H∞ exponential synchronization for delayed semi-Markov jump CDNs: A looped-functional approach," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    4. Han, Xin-Xin & Wu, Kai-Ning & Ding, Xiaohua, 2020. "Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    5. Wang, Dongji & Chen, Fei & Meng, Bo & Hu, Xingliu & Wang, Jing, 2021. "Event-based secure H∞ load frequency control for delayed power systems subject to deception attacks," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    6. Kwon, O.M. & Lee, S.H. & Park, M.J. & Lee, S.M., 2020. "Augmented zero equality approach to stability for linear systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    7. Liao, Wei & Liang, Taotao & Wang, Chen & Yang, Dayong, 2023. "A dimensionality reduction method for computing reachable tubes based on piecewise pseudo-time dependent Hamilton–Jacobi equation," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    8. Zhang, Liang & Feng, Zhiguang & Jiang, Zhengyi & Zhao, Ning & Yang, Yang, 2020. "Improved results on reachable set estimation of singular systems," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    9. Suriguga, & Kao, Yonggui & Shao, Chuntao & Chen, Xiangyong, 2021. "Stability of high-order delayed Markovian jumping reaction-diffusion HNNs with uncertain transition rates," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    10. Zhang, Huasheng & Zhuang, Guangming & Sun, Wei & Li, Yongmin & Lu, Junwei, 2020. "pth moment asymptotic interval stability and stabilization of linear stochastic systems via generalized H-representation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    11. Song, Xingxing & Lu, Hongqian & Xu, Yao & Zhou, Wuneng, 2022. "H∞ synchronization of semi-Markovian jump neural networks with random sensor nonlinearities via adaptive event-triggered output feedback control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 1-19.
    12. Xia, Yude & Wang, Jing & Meng, Bo & Chen, Xiangyong, 2020. "Further results on fuzzy sampled-data stabilization of chaotic nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    13. Yang, Chengyu & Li, Fei & Kong, Qingkai & Chen, Xiangyong & Wang, Jian, 2021. "Asynchronous fault-tolerant control for stochastic jumping singularly perturbed systems: An H∞ sliding mode control scheme," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    14. Li, Qiang & Liang, Jinling, 2022. "Non-fragile asynchronous state estimation for Markovian switching CVNs with partly accessible mode detection: The discrete-time case," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    15. Chen, Ruihan & Guo, Moxuan & Zhu, Song & Qi, Yongqiang & Wang, Min & Hu, Junhao, 2022. "Reachable set bounding for linear systems with mixed delays and state constraints," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    16. Huang, Yanli & Hou, Jie & Yang, Erfu, 2020. "Passivity and Synchronization of Coupled Reaction-Diffusion Complex-Valued Memristive Neural Networks," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    17. Arthi, G. & Suganya, K., 2021. "Controllability of higher order stochastic fractional control delay systems involving damping behavior," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    18. Xi, Changjiang & Dong, Jiuxiang, 2021. "Adaptive asymptotic tracking control of uncertain nonlinear time-delay systems depended on delay estimation information," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    19. Liu, Guobao & Chen, Xiangyong & Shen, Zhongyu & Liu, Yajuan & Jia, Xianglei, 2022. "Reachable set estimation for continuous delayed singularly perturbed systems with bounded disturbances," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    20. Fang, Tian & Jiao, Shiyu & Fu, Dongmei & Su, Lei, 2021. "Passivity-based synchronization for Markov switched neural networks with time delays and the inertial term," Applied Mathematics and Computation, Elsevier, vol. 394(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:12:y:2024:i:17:p:2721-:d:1468345. 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.