IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v374y2020ics0096300319309932.html
   My bibliography  Save this article

SMC for semi-Markov jump T-S fuzzy systems with time delay

Author

Listed:
  • Gao, Meng
  • Zhang, Lihua
  • Qi, Wenhai
  • Cao, Jinde
  • Cheng, Jun
  • Kao, Yonggui
  • Wei, Yunliang
  • Yan, Xiaoyu

Abstract

This paper investigates the issue of robust stabilization for delayed semi-Markov jump T-S fuzzy systems via sliding mode control (SMC). In order to reduce some conservativeness, an integral sliding mode surface (ISMS) is designed without assumption that the input matrices are plat-rule independent with full column rank, which is one of the critical factors for system performance. Based on Lyapunov functional theory, sufficient condition is provided for stochastic stability of the closed-loop system, and then extended to the case where the input matrices are independent of plant-rule. In addition, a fuzzy SMC controller is established to guarantee the finite time reachability of the predetermined fuzzy manifold. Finally, the superiorities of the proposed method are validated by a single-link robot arm model.

Suggested Citation

  • Gao, Meng & Zhang, Lihua & Qi, Wenhai & Cao, Jinde & Cheng, Jun & Kao, Yonggui & Wei, Yunliang & Yan, Xiaoyu, 2020. "SMC for semi-Markov jump T-S fuzzy systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    • Handle: RePEc:eee:apmaco:v:374:y:2020:i:c:s0096300319309932
    DOI: 10.1016/j.amc.2019.125001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319309932
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.125001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cheng, Jun & Zhan, Yang, 2020. "Nonstationary l2−l∞ filtering for Markov switching repeated scalar nonlinear systems with randomly occurring nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    2. Min Li & Ming Liu & Yingchun Zhang & Yunhai Geng, 2018. "Fault tolerant sliding mode control for T-S fuzzy stochastic time-delay system via a novel sliding mode observer approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(7), pages 1353-1367, May.
    3. Ge, Chao & Shi, Yanpen & Park, Ju H. & Hua, Changchun, 2019. "Robust H∞ stabilization for T-S fuzzy systems with time-varying delays and memory sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 500-512.
    4. Qi, Wenhai & Yang, Xu & Gao, Xianwen & Cheng, Jun & Kao, Yonggui & Wei, Yunliang, 2020. "Stability for delayed switched systems with Markov jump parameters and generally incomplete transition rates," Applied Mathematics and Computation, Elsevier, vol. 365(C).
    5. Wang, Jimin & Ma, Shuping & Zhang, Chenghui, 2016. "Stability analysis and stabilization for nonlinear continuous-time descriptor semi-Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 90-102.
    6. Ran, Suzhen & Xue, Yanmei & Zheng, Bo-Chao & Wang, Zhenyou, 2017. "Quantized feedback fuzzy sliding mode control design via memory-based strategy," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 283-295.
    7. Wang, Yangling & Cao, Jinde & Wang, Haijun & Alsaadi, Fuad E., 2019. "Event-triggered consensus of multi-agent systems with nonlinear dynamics and communication delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 147-157.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Harshavarthini, S. & Kwon, O.M. & Lee, S.M., 2022. "Uncertainty and disturbance estimator-based resilient tracking control design for fuzzy semi-Markovian jump systems," Applied Mathematics and Computation, Elsevier, vol. 426(C).
    2. Lee, Won Il & Park, Bum Yong & Kim, Sung Hyun, 2022. "Relaxed observer-based stabilization and dissipativity conditions of T-S fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    3. Wang, Xingxing & Ma, Yuechao, 2023. "Adaptive non-fragile sliding mode control for switched semi-Markov jump system with time-delay and attack via reduced-order method," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    4. Visakamoorthi, B. & Subramanian, K. & Muthukumar, P., 2022. "Hidden Markov model based non-fragile sampled-data control design for mode-dependent fuzzy systems with actuator faults," Applied Mathematics and Computation, Elsevier, vol. 435(C).

    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. Wang, Bo & Cheng, Jun & Zhou, Xia, 2020. "A multiple hierarchical structure strategy to quantized control of Markovian switching systems," Applied Mathematics and Computation, Elsevier, vol. 373(C).
    2. Luo, Jinnan & Liu, Xinzhi & Tian, Wenhong & Zhong, Shouming & Shi, Kaibo & Cheng, Jun, 2020. "A new approach to generalized dissipativity analysis for fuzzy systems with coupling memory sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    3. Ren, Junchao & Feng, Lihong & Fu, Jun & Zhuang, Tianyu, 2021. "Admissibility analysis and passive output feedback control for one-sided Lipschitz nonlinear singular Markovian jump systems with uncertainties," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. 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).
    5. Wang, Yuxiao & Cao, Yuting & Guo, Zhenyuan & Wen, Shiping, 2020. "Passivity and passification of memristive recurrent neural networks with multi-proportional delays and impulse," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    6. Zhang, Jie & Sun, Yuangong & Meng, Fanwei, 2020. "State bounding for discrete-time switched nonlinear time-varying systems using ADT method," Applied Mathematics and Computation, Elsevier, vol. 372(C).
    7. Aravindh, D. & Sakthivel, R. & Kong, Fanchao & Marshal Anthoni, S., 2020. "Finite-time reliable stabilization of uncertain semi-Markovian jump systems with input saturation," Applied Mathematics and Computation, Elsevier, vol. 384(C).
    8. Xue, Yanmei & Ren, Wen & Zheng, Bo-Chao & Han, Jinke, 2022. "Event-triggered adaptive sliding mode control of cyber-physical systems under false data injection attack," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    9. de Oliveira, Fúlvia S.S. & Souza, Fernando O., 2020. "Further refinements in stability conditions for time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    10. Haghighi, Payam & Tavassoli, Babak & Farhadi, Alireza, 2020. "A practical approach to networked control design for robust H∞ performance in the presence of uncertainties in both communication and system," Applied Mathematics and Computation, Elsevier, vol. 381(C).
    11. Cai, Yuliang & Zhang, Huaguang & Liu, Yang & He, Qiang, 2020. "Distributed bipartite finite-time event-triggered output consensus for heterogeneous linear multi-agent systems under directed signed communication topology," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    12. Xue, Yanmei & Zheng, Bo-Chao & Li, Tao & Li, Yuanlu, 2017. "Robust adaptive state feedback sliding-mode control of memristor-based Chua’s systems with input nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 142-153.
    13. Xu, Tianbo & Gao, Xianwen & Qi, Wenhai & Wei, Yunliang, 2019. "Disturbance-observer-based control for semi-Markovian jump systems with generally uncertain transition rate and saturation nonlinearity," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    14. Wu, Yuyan & Cheng, Jun & Zhou, Xia & Cao, Jinde & Luo, Mengzhuo, 2021. "Asynchronous filtering for nonhomogeneous Markov jumping systems with deception attacks," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    15. Kwon, Nam Kyu & Park, In Seok & Park, PooGyeon, 2017. "H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 126-135.
    16. Khan, Wakeel & Lin, Yan & Ullah Khan, Sarmad & Ullah, Nasim, 2018. "Quantized adaptive decentralized control for interconnected nonlinear systems with actuator faults," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 175-189.
    17. Ye, Dan & Li, Xiehuan, 2020. "Event-triggered fault detection for continuous-time networked polynomial-fuzzy-model-based systems," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    18. Jia, You & Wu, Huaiqin & Cao, Jinde, 2020. "Non-fragile robust finite-time synchronization for fractional-order discontinuous complex networks with multi-weights and uncertain couplings under asynchronous switching," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    19. Luo, Jinnan & Liu, Xinzhi & Tian, Wenhong & Zhong, Shouming & Shi, Kaibo & Li, Mengling, 2020. "Finite-time H∞ reliable control for T–S fuzzy systems with variable sampling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    20. Chu, Xiaoan & Li, Muguo, 2019. "Observer-based model following sliding mode tracking control of discrete-time linear networked systems with two-channel event-triggered schemes and quantizations," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 428-448.

    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:eee:apmaco:v:374:y:2020:i:c:s0096300319309932. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.