IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v45y2012i1p56-62.html
   My bibliography  Save this article

A generalized Halanay inequality on impulsive delayed dynamical systems and its applications

Author

Listed:
  • Wu, Quanjun
  • Zhang, Hua
  • Xiang, Lan
  • Zhou, Jin

Abstract

The main objective of this paper is to extend previous results on Halanay inequality for impulsive delayed dynamical systems. Based on the Razumikhin technique, a generalized Halanay differential inequality on impulsive delayed dynamical systems is analytically established. Compared with some existing works, the distinctive feature of this work is that it can be used to stabilize an unstable delayed dynamical system via impulses. The generalized Halanay inequality may be applied to secure communication systems, and a numerical example is given for illustrating and interpreting the theoretical results.

Suggested Citation

  • Wu, Quanjun & Zhang, Hua & Xiang, Lan & Zhou, Jin, 2012. "A generalized Halanay inequality on impulsive delayed dynamical systems and its applications," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 56-62.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:1:p:56-62
    DOI: 10.1016/j.chaos.2011.09.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077911001937
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2011.09.010?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. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Global synchronization in general complex delayed dynamical networks and its applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 729-742.
    2. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Synchronization in complex delayed dynamical networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 684-692.
    3. Lu, Junwei & Guo, Yiqian & Xu, Shengyuan, 2006. "Global asymptotic stability analysis for cellular neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 349-353.
    4. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2006. "Stability analysis for cellular neural networks with variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 331-336.
    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. Ma, Mihua & Zhou, Jin & Cai, Jianping, 2014. "Impulsive practical tracking synchronization of networked uncertain Lagrangian systems without and with time-delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 116-132.
    2. Sheng, Li & Yang, Huizhong, 2009. "Robust stability of uncertain Markovian jumping Cohen–Grossberg neural networks with mixed time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2120-2128.
    3. Zhang, Lan & Yang, Xinsong & Xu, Chen & Feng, Jianwen, 2017. "Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 22-30.
    4. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2008. "Delay-dependent exponential stability criteria for non-autonomous cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 985-990.
    5. Li, Yongkun & Xing, Zhiwei, 2007. "Existence and global exponential stability of periodic solution of CNNs with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1686-1693.
    6. Chu, Tianguang & Yang, Haifeng, 2007. "A note on exponential convergence of neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1538-1545.
    7. Singh, Vimal, 2007. "Some remarks on global asymptotic stability of neural networks with constant time delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1720-1724.
    8. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2009. "Global exponential stability for nonautonomous cellular neural networks with unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1144-1151.
    9. Singh, Vimal, 2007. "Global asymptotic stability of neural networks with delay: Comparative evaluation of two criteria," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1187-1190.
    10. Xiong, Wenjun & Liang, Jinling, 2007. "Novel stability criteria for neutral systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1735-1741.
    11. Singh, Vimal, 2007. "Simplified approach to the exponential stability of delayed neural networks with time varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 609-616.
    12. Wu, Quanjun & Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2009. "Impulsive control and synchronization of chaotic Hindmarsh–Rose models for neuronal activity," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2706-2715.
    13. Singh, Vimal, 2007. "Novel LMI condition for global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 503-508.
    14. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    15. Singh, Vimal, 2007. "On global exponential stability of delayed cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 188-193.
    16. Yu, Tianhu & Cao, Dengqing & Yang, Yang & Liu, Shengqiang & Huang, Wenhu, 2016. "Robust synchronization of impulsively coupled complex dynamical network with delayed nonidentical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 92-101.
    17. Peng, Dezhong & Yi, Zhang, 2008. "Global convergence of an adaptive minor component extraction algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 550-561.
    18. Gao, Ming & Cui, Baotong, 2009. "Global robust stability of neural networks with multiple discrete delays and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1823-1834.
    19. Chen, Zhang, 2009. "Complete synchronization for impulsive Cohen–Grossberg neural networks with delay under noise perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1664-1669.
    20. Singh, Vimal, 2007. "Global robust stability of delayed neural networks: Estimating upper limit of norm of delayed connection weight matrix," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 259-263.

    More about this item

    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:45:y:2012:i:1:p:56-62. 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.