Skip to main content
SpringerLink
Log in

Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, a class of uncertain neutral high-order stochastic Hopfield neural networks with time-varying delays is investigated. By using Lyapunov-Krasovskii functional and stochastic analysis approaches, new and less conservative delay-dependent stability criteria is presented in terms of linear matrix inequalities to guarantee the neural networks to be globally robustly exponentially stable in the mean square for all admissible parameter uncertainties and stochastic perturbations. Numerical simulations are carried out to illustrate the main results.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Blythe S, Mao X, Liao X (2001) Stability of stochastic delay neural networks. J Franklin Inst 338: 481–495

    Article  MATH  MathSciNet  Google Scholar 

  2. Boyd S, EI Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia, PA

    MATH  Google Scholar 

  3. Cao J, Song Q (2006) Stability in Cohen-Grossberg-type bidirectional associative memory neural networks with time-varying delays. Nonlinearity 19: 1601–1617

    Article  MATH  MathSciNet  Google Scholar 

  4. Chen Z, Zhao D, Ruan J (2007) Dynamic analysis of high-order Cohen-Grossberg neural networks with time delay. Chaos Solitons Fractals 32: 1538–1546

    Article  MATH  MathSciNet  Google Scholar 

  5. Gopalsamy K, He X (1994) Stability in asymmetric Hopfield neural networks with transmission delays. Physica D 76: 344–398

    Article  MATH  MathSciNet  Google Scholar 

  6. Gu K (2000) An integral inequality in the stability problem of time-delay system. In: Processings of 39th IEEE conference on decision and control. Sydney, Australia, pp 2805–2810

  7. Hale J (1977) Theory of functional differential equations. Springer-Verlag, New York

    MATH  Google Scholar 

  8. Hale J, Verduyn Lunel SM (1993) Introdution to functional differential equations. Springer-Verlag, New York

    Google Scholar 

  9. Hopfield J (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci USA 79: 2554–2558

    Article  MathSciNet  Google Scholar 

  10. Hopfield J (1984) Neurons with graded response have collective computational properties like those of two-state neurons. Proc Nat Acad Sci USA 81: 3088–3092

    Article  Google Scholar 

  11. Liu B, Huang L (2007) Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays. Chaos Solitons Fractals 31: 211–217

    Article  MATH  MathSciNet  Google Scholar 

  12. Liu Y, Wang Z, Liu X (2006) On global exponential stability of generalized stochastic neural networks with mixed time-delays. Neurocomputing 70: 314–326

    Article  Google Scholar 

  13. Lou X, Cui B (2007) Novel global stability criteria for high-order Hopfield-type neural networks with time-varying delays. J Math Anal Appl 330: 144–158

    Article  MATH  MathSciNet  Google Scholar 

  14. Ren F, Cao J, Qiu J (2006) LMI-based criteria for stability of high-order neural networks with time-varying delay. Nonlinear Anal Real World Appl 7: 967–979

    Article  MATH  MathSciNet  Google Scholar 

  15. Song Y, Han M, Wei J (2005) Stability and Hopf bifurcation analysis on a simplified BAM neural network with delays. Physica D 200: 185–204

    Article  MATH  MathSciNet  Google Scholar 

  16. Wang Y, Xie L, de Souza CE (1992) Robust control of a class of uncertain nonlinear system. Syst Control Lett 19(2): 139–149

    Article  Google Scholar 

  17. Wang Z, Lauria S, Fang J, Liu X (2007) Exponential stability of uncertain stochastic neural networks with mixed time-delays. Chaos Solitons Fractals 32: 62–72

    Article  MATH  MathSciNet  Google Scholar 

  18. Wang Z, Fang J, Liu X (2008) Global stability of stochastic high-order neural networks with discrete and distributed delays. Chaos Solitons Fractals 36: 388–396

    Article  MATH  MathSciNet  Google Scholar 

  19. Xu B, Wang Q, Liao X (2008) Stability analysis of high-order Hopfield type neural networks with uncertainty. Neurocomputing 71: 508–512

    Article  Google Scholar 

  20. Zhao H, Ding N (2007) Dynamic analysis of stochastic bidirectional associative memory neural networks with delays. Chaos Solitons Fractals 32: 1692–1702

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, 97 Heping West Road, Shijiazhuang, Hebei Province, 050003, People’s Republic of China

    Qintao Gan & Rui Xu

Authors
  1. Qintao Gan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qintao Gan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gan, Q., Xu, R. Global Robust Exponential Stability of Uncertain Neutral High-Order Stochastic Hopfield Neural Networks with Time-Varying Delays. Neural Process Lett 32, 83–96 (2010). https://doi.org/10.1007/s11063-010-9146-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-010-9146-9

Keywords

Search

Navigation