IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v392y2021ics0096300320306494.html
   My bibliography  Save this article

Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm

Author

Listed:
  • Jia, Jinping
  • Dai, Hao
  • Li, Li
  • Zhang, Fandi

Abstract

In this paper, the problem of global sampled-data stabilization is investigated for high-order nonlinear systems with arbitrarily long input delays. Based on the Lie algebra technique in nonlinear control theory, a discrete-time predictor-based multi-rate sampled-data state feedback control law with a series expansion form is proposed to ensure that the resulting system is globally asymptotically stable under some conditions. Compared with the existing methods, the proposed control algorithm just needs to know the approximate prediction of state variables, and the faster decrease of Lyapunov function may be provided for each subsystem. Performance of approximate versions of the proposed controller is given by theoretical analyses. It is showed that the approximate controllers achieve practical stability of the sampled-data closed-loop system. Finally, the obtained stabilization results are applied to a trajectory tracking problem for a high-order planar system.

Suggested Citation

  • Jia, Jinping & Dai, Hao & Li, Li & Zhang, Fandi, 2021. "Global sampled-data stabilization for a class of nonlinear systems with arbitrarily long input delays via a multi-rate control algorithm," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306494
    DOI: 10.1016/j.amc.2020.125696
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320306494
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125696?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. Fang, Liandi & Ma, Li & Ding, Shihong & Zhao, Dean, 2019. "Finite-time stabilization for a class of high-order stochastic nonlinear systems with an output constraint," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 63-79.
    2. Li, Wenhua & Gao, Xingbao & Li, Ruoxia, 2020. "Stability and synchronization control of inertial neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    3. Liu, Wenhui & Lu, Junwei & Xu, Shengyuan & Li, Yongmin & Zhang, Zhengqiang, 2019. "Sampled-data controller design and stability analysis for nonlinear systems with input saturation and disturbances," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 14-27.
    4. Pan, Yingnan & Yang, Guang-Hong, 2019. "Event-based reduced-order fuzzy filtering for networked control systems with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 71-83.
    5. 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.
    6. Yuan-Xin Li & Guang-Hong Yang & Shaocheng Tong, 2018. "Event-triggered adaptive fuzzy tracking control of nonlinear MIMO systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(12), pages 2618-2629, September.
    7. Yang Wang & Jinna Li & Xiaolei Ji, 2018. "Tracking Control of Fuzzy Dynamic Output for Nonlinear Networked System with Packet Dropouts," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-10, January.
    8. 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).
    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. 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).
    2. Cui, Lili & Zhang, Yong & Wang, Xiaowei & Xie, Xiangpeng, 2021. "Event-triggered distributed self-learning robust tracking control for uncertain nonlinear interconnected systems," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    3. 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).
    4. Mei, Keqi & Ding, Shihong, 2022. "Output-feedback finite-time stabilization of a class of constrained planar systems," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    5. Yao, Hejun & Gao, Fangzheng & Huang, Jiacai & Wu, Yuqiang, 2021. "Global prescribed-time stabilization via time-scale transformation for switched nonlinear systems subject to switching rational powers," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    6. 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).
    7. Zhang, Shuo & Liu, Lu & Xue, Dingyu, 2020. "Nyquist-based stability analysis of non-commensurate fractional-order delay systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).
    8. Yang, Yi & Chen, Fei & Lang, Jiahong & Chen, Xiangyong & Wang, Jing, 2021. "Sliding mode control of persistent dwell-time switched systems with random data dropouts," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    9. 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).
    10. Vadivel, R. & Sabarathinam, S. & Wu, Yongbao & Chaisena, Kantapon & Gunasekaran, Nallappan, 2022. "New results on T–S fuzzy sampled-data stabilization for switched chaotic systems with its applications," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    11. Samer Al-Ghour & Dina Abuzaid & Monia Naghi, 2024. "Soft Weakly Quasi-Continuous Functions Between Soft Topological Spaces," Mathematics, MDPI, vol. 12(20), pages 1-19, October.
    12. Anto Anbarasu Yesudhas & Seong Ryong Lee & Jae Hoon Jeong & Narayanan Govindasami & Young Hoon Joo, 2024. "The Stabilization of a Nonlinear Permanent-Magnet- Synchronous-Generator-Based Wind Energy Conversion System via Coupling-Memory-Sampled Data Control with a Membership-Function-Dependent H ∞ Approach," Energies, MDPI, vol. 17(15), pages 1-21, July.
    13. Zuo, Zhiqiang & Xie, Pengfei & Wang, Yijing, 2020. "Output-based dynamic event-triggering control for sensor saturated systems with external disturbance," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    14. Zhang, He & Xu, Shengyuan & Zhang, Zhengqiang & Chu, Yuming, 2022. "Practical stability of a nonlinear system with delayed control input," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    15. Wang, Yingchun & Zhang, Jiaxin & Zhang, Huaguang & Xie, Xiangpeng, 2021. "Finite-time adaptive neural control for nonstrict-feedback stochastic nonlinear systems with input delay and output constraints," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    16. Abinandhitha, R. & Monisha, S. & Sakthivel, R. & Manikandan, R. & Saat, S., 2023. "Proportional integral observer-based input–output finite-time stabilization for chaotic semi-Markov jump fuzzy systems," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    17. Zhang, Haoyue & Ding, Shihong, 2023. "Adaptive asymptotic tracking control design for high-order uncertain nonlinear systems," Applied Mathematics and Computation, Elsevier, vol. 445(C).
    18. Han, S.Y. & Kommuri, S.K. & Kwon, O.M. & Lee, S.M., 2022. "Regional sampled-data synchronization of chaotic neural networks using piecewise-continuous delay dependent Lyapunov functional," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    19. Wang, Haitao & Chen, Xiangyong & Wang, Jing, 2022. "H∞ sliding mode control for PDT-switched nonlinear systems under the dynamic event-triggered mechanism," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    20. Kaviarasan, Boomipalagan & Kwon, Oh-Min & Park, Myeong Jin & Sakthivel, Rathinasamy, 2023. "Reduced-order filtering for semi-Markovian jump systems against randomly occurring false data injection attacks," Applied Mathematics and Computation, Elsevier, vol. 444(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:eee:apmaco:v:392:y:2021:i:c:s0096300320306494. 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.