Skip to main content
SpringerLink
Log in

Mean Square Exponential Stability of Uncertain Stochastic Hopfield Neural Networks with Interval Time-Varying Delays

  • Conference paper
Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence (ICIC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4682))

Included in the following conference series:

  • 1745 Accesses

Abstract

The problem of mean square exponential stability of uncertain stochastic Hopfield neural networks with interval time-varying delays is investigated in this paper. The delay factor is assumed to be time-varying and belongs to a given interval, which means that the derivative of the delay function can exceed one. The uncertainties considered in this paper are norm-bounded and possibly time-varying. By Lyapunov-Krasovskii functional approach and stochastic analysis approach, a new delay-dependent stability criteria for the exponential stability of stochastic Hopfield neural networks is derived in terms of linear matrix inequalities(LMIs). A simulation example is given to demonstrate the effectiveness of the developed techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Hopfield, J.J.: Neural Networks And Physical Systems with Emergent Collect Computational Abilities. Proc. Nat. Acad. Sci. USA 79(2), 2554–2558 (1982)

    Article  MathSciNet  Google Scholar 

  2. Wang, Z., Shu, H., Fang, J., Liu, X.: Robust Stability For Stochastic Hopfield Neural Networks With Time Delays. Nonlinear Analysis: Real World Applications 7(5), 1119–1128 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  3. Liao, X., Wong, K., Li, C.: Global Exponential Stability For A Class Of Generalized Neural Networks With Distributed Delays. Nonlinear Analysis: Real World Applications 5(3), 527–547 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  4. Song, Q., Wang, Z.: An Analysis On Existence And Global Exponential Stability Of Periodic Solutions For BAM Neural Networks With Time-Varying Delays. Nonlinear Analysis: Real World Applications (2006) (in press)

    Google Scholar 

  5. Singh, V.: On Global Robust Stability Of Interval Hopfield Neural Networks With Delay. Chaos, Solitons and Fractals 33(4), 1183–1188 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Qiu, J., Yang, H., Zhang, J., Gao, Z.: New Robust Stability Criteria For Uncertain Neural Networks With Interval Time-Varying Delays. Chaos, Solitons and Fractals (2007) (in press)

    Google Scholar 

  7. Qiu, J., Zhang, J.: New Robust Stability Criterion For Uncertain Fuzzy Systems With Fast Time-Varying Delays. In: Selman, A.L. (ed.) Structure in Complexity Theory. LNCS, vol. 223(4), pp. 41–44. Springer, Heidelberg (1986)

    Google Scholar 

  8. Qiu, J., Zhang, J., Shi, P.: Robust Stability Of Uncertain Linear Systems With Time-Varying Delay And Nonlinear Perturbations. Proceedings of The Institution of Mechanical Engineers Part I: Journal of Systems and Control Engineering 220(5), 411–416 (2006)

    Article  Google Scholar 

  9. Lou, X., Cui, B.: Delay-Dependent Stochastic Stability Of Delayed Hopfield Neural Networks With Markovian Jump Parameters. Journal of Mathematical Analysis and Applications 328(1), 316–326 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  10. Wang, Z., Liu, Y., Yu, L., Liu, X.: Exponential Stability Of Delayed Recurrent Neural Networks With Markovian Jumping Parameters. Physics Letters A 356(4-5), 346–352 (2006)

    Article  MATH  Google Scholar 

  11. Zhang, J., Shi, P., Qiu, J.: Robust Stability Criteria For Uncertain Neutral System With Time Delay and Nonlinear Uncertainties. Chaos, Solitons and Fractals (2006) ( in press)

    Google Scholar 

  12. Wang, Z., Liu, Y., Fraser, K., Liu, X.: Stochastic Stability Of Uncertain Hopfield Neural Networks With Discrete And Distributed Delays. Physics Letters A 354(4-5), 288–297 (2006)

    Article  Google Scholar 

  13. Ou, O.: Global Robust Exponential Stability Of Delayed Neural Networks: An LMI Approach. Chaos, Solitons and Fractals 32(5), 1742–1748 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mohamad, S.: Exponential Stability In Hopfield-Type Neural Networks With Impulses. Chaos, Solitons and Fractals 32(2), 456–467 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  15. Jiang, X., Han, Q.-L.: On H  ∞  Control For Linear Systems With Interval Time-Varying Delay. Automatica 41(12), 2099–2106 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  16. Barmish, B.R.: Necessary And Sufficient Conditions For Quadratic Stability Of An Uncertain System. Journal of Optimal Theory Apply 46(12), 2147–2152 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Sciences, Hebei University of Science and Technology, Shijiazhuang, 050018, China

    Jiqing Qiu & Hongjiu Yang

  2. Department of Automatic Control, Beijing Institute of Technology, Beijing 100081, China

    Yuanqing Xia & Jinhui Zhang

Authors
  1. Jiqing Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongjiu Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuanqing Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jinhui Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

De-Shuang Huang Laurent Heutte Marco Loog

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Qiu, J., Yang, H., Xia, Y., Zhang, J. (2007). Mean Square Exponential Stability of Uncertain Stochastic Hopfield Neural Networks with Interval Time-Varying Delays. In: Huang, DS., Heutte, L., Loog, M. (eds) Advanced Intelligent Computing Theories and Applications. With Aspects of Artificial Intelligence. ICIC 2007. Lecture Notes in Computer Science(), vol 4682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74205-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74205-0_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74201-2

  • Online ISBN: 978-3-540-74205-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation