IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v435y2022ics0096300322005355.html
   My bibliography  Save this article

Algebra criteria for global exponential stability of multiple time-varying delay Cohen–Grossberg neural networks

Author

Listed:
  • Zhang, Zhongjie
  • Yu, Tingting
  • Zhang, Xian

Abstract

This paper aims at establishing global exponential stability criteria for multiple time-varying delay Cohen–Grossberg neural networks (CGNNs). The considered network models cannot be expressed as the vector-matrix form, which yields that many methods in literature are unavailable. By constructing novel Lyapunov–Krasovskii functionals, two novel algebraic criteria guaranteeing global exponential stability of CGNNs under consideration are given. A pair of numerical examples are used to explain the effectiveness of the obtained algebra criteria relative to the previously stability conditions. It is worth emphasizing that the approach applied in this paper is applicable to CGNNs that may or may not be represented in vector-matrix form.

Suggested Citation

  • Zhang, Zhongjie & Yu, Tingting & Zhang, Xian, 2022. "Algebra criteria for global exponential stability of multiple time-varying delay Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 435(C).
    • Handle: RePEc:eee:apmaco:v:435:y:2022:i:c:s0096300322005355
    DOI: 10.1016/j.amc.2022.127461
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322005355
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127461?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. Manivannan, R. & Samidurai, R. & Cao, Jinde & Alsaedi, Ahmed & Alsaadi, Fuad E., 2018. "Stability analysis of interval time-varying delayed neural networks including neutral time-delay and leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 433-445.
    2. Wu, Wei & Cui, Bao Tong & Huang, Min, 2007. "Global asymptotic stability of Cohen–Grossberg neural networks with constant and variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1355-1361.
    3. Chen, Yonghui & Zhang, Xian & Xue, Yu, 2022. "Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 173-189.
    4. Wang, Junlan & Wang, Xin & Wang, Yantao & Zhang, Xian, 2021. "Non-reduced order method to global h-stability criteria for proportional delay high-order inertial neural networks," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    5. Qiu, Jiqing & Yang, Hongjiu & Zhang, Jinhui & Gao, Zhifeng, 2009. "New robust stability criteria for uncertain neural networks with interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 579-585.
    6. Li, Ruoxia & Cao, Jinde & Xue, Changfeng & Manivannan, R., 2021. "Quasi-stability and quasi-synchronization control of quaternion-valued fractional-order discrete-time memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    7. Chen, Shengshuang & Zhao, Weirui & Xu, Yong, 2009. "New criteria for globally exponential stability of delayed Cohen–Grossberg neural network," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1527-1543.
    8. Udhayakumar, K. & Rakkiyappan, R. & Li, Xiaodi & Cao, Jinde, 2021. "Mutiple ψ-type stability of fractional-order quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    9. Dong, Zeyu & Wang, Xin & Zhang, Xian, 2020. "A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen–Grossberg neural networks," Applied Mathematics and Computation, Elsevier, vol. 385(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. Chen, Yonghui & Xue, Yu & Yang, Xiaona & Zhang, Xian, 2023. "A direct analysis method to Lagrangian global exponential stability for quaternion memristive neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    2. Meng, Xianhe & Zhang, Xian & Wang, Yantao, 2023. "Bounded real lemmas and exponential H∞ control for memristor-based neural networks with unbounded time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 66-81.
    3. Zhang, Xiao-Li & Li, Hong-Li & Kao, Yonggui & Zhang, Long & Jiang, Haijun, 2022. "Global Mittag-Leffler synchronization of discrete-time fractional-order neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    4. Chang, Shuang & Wang, Yantao & Zhang, Xian & Wang, Xin, 2023. "A new method to study global exponential stability of inertial neural networks with multiple time-varying transmission delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 329-340.
    5. Mo, Wenjun & Bao, Haibo, 2022. "Finite-time synchronization for fractional-order quaternion-valued coupled neural networks with saturated impulse," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Hua, Wentao & Wang, Yantao & Liu, Chunyan, 2024. "New method for global exponential synchronization of multi-link memristive neural networks with three kinds of time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 471(C).
    7. Zhang, Hai & Cheng, Yuhong & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2022. "Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 341-357.
    8. Yang, Jinrong & Chen, Guici & Wen, Shiping & Wang, Leimin, 2023. "Finite-time dissipative control for discrete-time memristive neural networks via interval matrix method," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    9. Zhang, Zhengqiu & Yang, Zhen, 2023. "Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    10. Duan, Lian & Liu, Jinzhi & Huang, Chuangxia & Wang, Zengyun, 2022. "Finite-/fixed-time anti-synchronization of neural networks with leakage delays under discontinuous disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    11. Chen, Yonghui & Zhang, Xian & Xue, Yu, 2022. "Global exponential synchronization of high-order quaternion Hopfield neural networks with unbounded distributed delays and time-varying discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 173-189.
    12. Chang, Wenting & Sang, Hong & Guo, Liangdong & Wu, Libing & Dimirovski, Georgi M., 2024. "Integrated L∞ anti-disturbance synchronization control for switched neural networks with unknown delays," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    13. Gao, Ming & Cui, Baotong, 2009. "Robust exponential stability of interval Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1914-1928.
    14. Zeng, Runtian & Song, Qiankun, 2024. "Mean-square exponential input-to-state stability for stochastic neutral-type quaternion-valued neural networks via Itô’s formula of quaternion version," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    15. Otkel, Madina & Ganesan, Soundararajan & Rajan, Rakkiyappan & Kashkynbayev, Ardak, 2024. "Finite-time/fixed-time synchronization of memristive shunting inhibitory cellular neural networks via sliding mode control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 252-263.
    16. Wang, Fen & Chen, Yuanlong, 2021. "Mean square exponential stability for stochastic memristor-based neural networks with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    17. Zhao, Mingfang & Li, Hong-Li & Zhang, Long & Hu, Cheng & Jiang, Haijun, 2023. "Quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks with time delays and uncertain parameters," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    18. Wen, Zhen & Sun, Jitao, 2009. "Stability analysis of delayed Cohen–Grossberg BAM neural networks with impulses via nonsmooth analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1829-1837.
    19. Xie, Lifei & Cheng, Jun & Wang, Hailing & Wang, Jiange & Hu, Mengjie & Zhou, Zhidong, 2022. "Memory-based event-triggered asynchronous control for semi-Markov switching systems," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    20. Yang, Liu & Ma, Weijun & Wang, Xin, 2024. "Lagrange stability and passivity in the mean square sense of discrete-time stochastic Markovian switched neural networks with time-varying mixed delays," Applied Mathematics and Computation, Elsevier, vol. 477(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:435:y:2022:i:c:s0096300322005355. 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.