IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v39y2009i1p240-247.html
   My bibliography  Save this article

Improved asymptotic stability analysis for uncertain delayed state neural networks

Author

Listed:
  • Souza, Fernando O.
  • Palhares, Reinaldo M.
  • Ekel, Petr Ya.

Abstract

This paper presents a new linear matrix inequality (LMI) based approach to the stability analysis of artificial neural networks (ANN) subject to time-delay and polytope-bounded uncertainties in the parameters. The main objective is to propose a less conservative condition to the stability analysis using the Gu’s discretized Lyapunov–Krasovskii functional theory and an alternative strategy to introduce slack matrices. Two computer simulations examples are performed to support the theoretical predictions. Particularly, in the first example, the Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability. The second example is presented to illustrate how the proposed approach can provide better stability performance when compared to other ones in the literature.

Suggested Citation

  • Souza, Fernando O. & Palhares, Reinaldo M. & Ekel, Petr Ya., 2009. "Improved asymptotic stability analysis for uncertain delayed state neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 240-247.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:1:p:240-247
    DOI: 10.1016/j.chaos.2007.01.110
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907002330
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.01.110?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. Singh, Vimal, 2007. "Improved global robust stability criterion for delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 224-229.
    2. Singh, Vimal, 2006. "Simplified LMI condition for global asymptotic stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 470-473.
    3. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
    4. Cao, Jinde & Ho, Daniel W.C., 2005. "A general framework for global asymptotic stability analysis of delayed neural networks based on LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1317-1329.
    5. Arik, Sabri, 2005. "Global robust stability analysis of neural networks with discrete time delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1407-1414.
    6. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "Delay-dependent exponential stability of cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1363-1369.
    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. Souza, Fernando O. & Palhares, Reinaldo M. & Ekel, Petr Ya., 2009. "Novel stability criteria for uncertain delayed Cohen–Grossberg neural networks using discretized Lyapunov functional," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2387-2393.
    2. Kalpana, M. & Balasubramaniam, P. & Ratnavelu, K., 2015. "Direct delay decomposition approach to synchronization of chaotic fuzzy cellular neural networks with discrete, unbounded distributed delays and Markovian jumping parameters," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 291-304.

    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. Singh, Vimal, 2009. "Novel global robust stability criterion for neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 348-353.
    2. Singh, Vimal, 2009. "Remarks on estimating upper limit of norm of delayed connection weight matrix in the study of global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2013-2017.
    3. Singh, Vimal, 2007. "Novel LMI condition for global robust stability of delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 503-508.
    4. Song, Qiankun & Wang, Zidong, 2008. "Neural networks with discrete and distributed time-varying delays: A general stability analysis," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1538-1547.
    5. 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.
    6. Gau, R.S. & Lien, C.H. & Hsieh, J.G., 2007. "Global exponential stability for uncertain cellular neural networks with multiple time-varying delays via LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1258-1267.
    7. Singh, Vimal, 2007. "On global exponential stability of delayed cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 188-193.
    8. Singh, Vimal, 2007. "On global robust stability of interval Hopfield neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1183-1188.
    9. Park, Ju H., 2008. "On global stability criterion of neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 444-449.
    10. Song, Qiankun, 2008. "Novel criteria for global exponential periodicity and stability of recurrent neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 720-728.
    11. Jiang, Yanhong & Yang, Bin & Wang, Jincheng & Shao, Cheng, 2009. "Delay-dependent stability criterion for delayed Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2133-2137.
    12. Singh, Vimal, 2007. "LMI approach to the global robust stability of a larger class of neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1927-1934.
    13. 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.
    14. Park, Ju H. & Lee, S.M. & Kwon, O.M., 2009. "On exponential stability of bidirectional associative memory neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1083-1091.
    15. Huang, Lihong & Guo, Zhenyuan, 2009. "Global convergence of periodic solution of neural networks with discontinuous activation functions," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2351-2356.
    16. Zong, Guangdeng & Liu, Jia, 2009. "New delay-dependent global robust stability conditions for interval neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2954-2964.
    17. Lien, Chang-Hua & Chung, Long-Yeu, 2007. "Global asymptotic stability for cellular neural networks with discrete and distributed time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1213-1219.
    18. Wang, Zidong & Lauria, Stanislao & Fang, Jian’an & Liu, Xiaohui, 2007. "Exponential stability of uncertain stochastic neural networks with mixed time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 62-72.
    19. Cui, Shihua & Zhao, Tao & Guo, Jie, 2009. "Global robust exponential stability for interval neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1567-1576.
    20. Wang, Weiwei & Cao, Jinde, 2006. "Synchronization in an array of linearly coupled networks with time-varying delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 197-211.

    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:39:y:2009:i:1:p:240-247. 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.