IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v200y2025ip2s0960077925011038.html

Asymptotic stabilization for the full-discrete temporal–spatial-fractional reaction–diffusion system with time-varying delay

Author

Listed:
  • Li, Xing-Yu
  • Yang, Zhan-Wen
  • Wu, Kai-Ning

Abstract

Under the designed state-feedback controller, the asymptotic stabilization problem is studied for the continuous, spatial semi-discrete and temporal–spatial full-discrete temporal–spatial-fractional reaction–diffusion systems with time-varying delay (DTSFRDSs). For the continuous DTSFRDS, the sufficient condition of asymptotic stability is developed through the fractional Halanay inequality based on the Lyapunov functional method. Using the finite element scheme, we construct the spatial semi-discrete DTSFRDS and derive a sufficient criterion to ensure asymptotic stability. Combined with the L1 scheme, the temporal–spatial full-discrete DTSFRDS is built. By deriving the discrete fractional lemma and the discrete fractional Halanay inequality, we provide a sufficient condition of asymptotic stability for the temporal–spatial full-discrete DTSFRDS. According to the obtained results, when the spatial step size h is sufficiently small, the stability of the continuous DTSFRDS can be inherited by the discrete DTSFRDSs under the state-feedback controller. Numerical example are provided to confirm the validity of our results.

Suggested Citation

  • Li, Xing-Yu & Yang, Zhan-Wen & Wu, Kai-Ning, 2025. "Asymptotic stabilization for the full-discrete temporal–spatial-fractional reaction–diffusion system with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 200(P2).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p2:s0960077925011038
    DOI: 10.1016/j.chaos.2025.117090
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925011038
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.117090?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Li, Jing & Zhu, Quanxin, 2023. "Event-triggered impulsive control of stochastic functional differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Liu, Xinliang & Wan, Shaoke & Fang, Bin & Li, Xiaohu, 2024. "Dynamics analysis of time-delayed nonlinear system with asymmetric stiffness," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    3. Du, Feifei & Lu, Jun-Guo, 2021. "Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    4. Yao, Zichen & Yang, Zhanwen & Cheng, Lixin, 2025. "On the stability preserving of L1 scheme to nonlinear time-fractional Schrödinger delay equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 231(C), pages 209-220.
    5. Liu, Xiang & Wang, Peiguang & Anderson, Douglas R., 2022. "On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(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. Wei, Yiheng & Su, Nan & Zhao, Linlin & Cao, Jinde, 2023. "LMI based stability condition for delta fractional order system with sector approximation," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Xia, Mingli & Liu, Linna & Fang, Jianyin & Qu, Boyang, 2024. "Exponentially weighted input-to-state stability of stochastic differential systems via event-triggered impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Zheng, Wei & Zhang, Zhiming & Lam, Hak-Keung & Sun, Fuchun & Wen, Shuhuan, 2023. "LMIs-based exponential stabilization for interval delay systems via congruence transformation: Application in chaotic Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    4. Nosrati, Komeil & Belikov, Juri & Tepljakov, Aleksei & Petlenkov, Eduard, 2023. "Extended fractional singular kalman filter," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    5. Lan Cheng & Ruiyang Cai & Jianping Huang & Huacheng Zhou, 2025. "A Note on Infinite Horizon Linear Quadratic Optimal Control Problems for Fractional-order System," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-15, August.
    6. Rui Kang & Shang Gao, 2022. "Stabilization for Stochastic Coupled Kuramoto Oscillators via Nonlinear Distributed Feedback Control," Mathematics, MDPI, vol. 10(18), pages 1-9, September.
    7. Di, Ying & Zhang, Jin-Xi & Zhang, Xuefeng, 2023. "Robust stabilization of descriptor fractional-order interval systems with uncertain derivative matrices," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    8. Wu, Yifan & Zhuang, Guangming & Jiang, Mengmeng & Wang, Yanqian, 2025. "H∞ adaptive ETF control for degenerate jump systems under actuator faults and impulsive deception attacks with application to DCMIP device," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    9. Xie, Xiang & Li, Xiaodi & Liu, Xinzhi, 2023. "Event-triggered impulsive control for multi-agent systems with actuation delay and continuous/periodic sampling," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    10. Wang, Feng-Xian & Zhang, Jie & Shu, Yan-Jun & Liu, Xin-Ge, 2023. "On stability and event trigger control of fractional neural networks by fractional non-autonomous Halanay inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:chsofr:v:200:y:2025:i:p2:s0960077925011038. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.