Skip to main content
Log in

Robust Stability in Cohen–Grossberg Neural Network with both Time-Varying and Distributed Delays

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this article, the global exponential robust stability is investigated for Cohen–Grossberg neural network with both time-varying and distributed delays. The parameter uncertainties are assumed to be time-invariant and bounded, and belong to given compact sets. Applying the idea of vector Lyapunov function, M-matrix theory and analysis techniques, several sufficient conditions are obtained to ensure the existence, uniqueness, and global exponential robust stability of the equilibrium point for the neural network. The methodology developed in this article is shown to be simple and effective for the exponential robust stability analysis of neural networks with time-varying delays and distributed delays. The results obtained in this article extend and improve a few recently known results and remove some restrictions on the neural networks. Three examples are given to show the usefulness of the obtained results that are less restrictive than recently known criteria.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans Syst Man Cybernet 13(5): 815–826

    MATH  MathSciNet  Google Scholar 

  2. Ye H, Michel AN, Wang K (1995) Qualitative analysis of Cohen–Grossberg neural networks with multiple delays. Phys Rev E 51(3): 2611–2618

    Article  ADS  MathSciNet  Google Scholar 

  3. Wang L, Zou XF (2002) Exponential stability of Cohen–Grossberg neural networks. Neural Netw 15(3): 415–422

    Article  Google Scholar 

  4. Wang L, Zou XF (2002) Harmless delays in Cohen–Grossberg neural networks. Physica D 170(2): 162–173

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. Lu WL, Chen TP (2003) New conditions on global stability of Cohen–Grossberg neural networks. Neural Comput 15(5): 1173–1189

    Article  MATH  Google Scholar 

  6. Chen TP, Rong LB (2003) Delay-independent stability analysis of Cohen–Grossberg neural networks. Phys Lett A 317(5–6): 436–449

    MATH  ADS  MathSciNet  Google Scholar 

  7. Liao XF, Li CG, Wong KW (2004) Criteria for exponential stability of Cohen–Grossberg neural networks. Neural Netw 17(10): 1401–1414

    Article  MATH  Google Scholar 

  8. Lu HT (2005) Global exponential stability analysis of Cohen–Grossberg neural networks. IEEE Trans Circuit Syst II 52(8): 476–479

    Article  Google Scholar 

  9. Guo SJ, Huang LH (2005) Stability analysis of Cohen–Grossberg neural networks. IEEE Trans Neural Netw 17(1): 106–117

    Article  Google Scholar 

  10. Rong LB (2005) LMI-based criteria for robust stability of Cohen–Grossberg neural networks with delay. Phys Lett A 339(1–2): 63–73

    Article  ADS  MathSciNet  Google Scholar 

  11. Yuan K, Cao JD (2005) An analysis of global asymptotic stability of delayed Cohen–Grossberg neural networks via nonsmooth analysis. IEEE Trans Circuit Syst I 52(9): 1854–1861

    Article  MathSciNet  Google Scholar 

  12. Cao JD, Li XL (2005) Stability in delayed Cohen–Grossberg neural networks: LMI optimization approach. Physica D 212(1–2): 54–65

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. Chen Y (2006) Global asymptotic stability of delayed Cohen–Grossberg neural networks. IEEE Trans Circuit Syst I 53(2): 351–357

    Article  Google Scholar 

  14. Liu J (2005) Global exponential stability of Cohen–Grossberg neural networks with time-varying delays. Chaos Solitons Fractal 26(3): 935–945

    Article  MATH  Google Scholar 

  15. Hwang CC, Cheng CJ, Liao TL (2003) Globally exponential stability of generalized Cohen–Grossberg neural networks with delays. Phys Lett A 319(1–2): 157–166

    Article  MATH  ADS  Google Scholar 

  16. Cao JD, Liang JL (2004) Boundedness and stability for Cohen–Grossberg neural network with time-varying delays. J Math Anal Appl 296(2): 665–685

    Article  MATH  MathSciNet  Google Scholar 

  17. Chen TP, Rong LB (2004) Robust global exponential stability of Cohen–Grossberg neural networks with time delays. IEEE Trans Neural Netw 15(1): 203–206

    Article  MathSciNet  Google Scholar 

  18. Arik S, Orman Z (2005) Global stability analysis of Cohen–Grossberg neural networks with time varying delays. Phys Lett A 314(5–6): 410–421

    Article  ADS  Google Scholar 

  19. Jiang MH, Shen Y, Liao XX (2006) Boundedness and global exponential stability for generalized Cohen–Grossberg neural networks with variable delay. Appl Math Comput 172(1): 379–393

    Article  MATH  MathSciNet  Google Scholar 

  20. Jiang HJ, Cao JD, Teng ZD (2006) Dynamics of Cohen–Grossberg neural networks with time-varying delays. Phys Lett A 354(5–6): 414–422

    Article  ADS  Google Scholar 

  21. Wang ZD, Liu YR, Liu XH (2005) On global asymptotic stability of neural networks with discrete and distributed delays. Phys Lett A 345(4–6): 299–308

    Article  ADS  Google Scholar 

  22. Wang ZD, Shu HS, Liu YR, Ho DWC, Liu XH (2006) Robust stability analysis of generalized neural networks with discrete and distributed time delays. Chaos Solitons Fractal 30(4): 886–896

    Article  MathSciNet  Google Scholar 

  23. Sun JH, Wan L (2005) Global exponential stability and periodic solutions of Cohen–Grossberg neural networks with continuously distributed delays. Physica D 208(1–2): 1–20

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. Wan L, Sun JH (2005) Global asymptotic stability of Cohen–Grossberg neural network with continuously distributed delays. Phys Lett A 342(4): 331–340

    Article  ADS  Google Scholar 

  25. Wang L (2005) Stability of Cohen–Grossberg neural networks with distributed delays. Appl Math Comput 160: 93–110

    Article  MATH  MathSciNet  Google Scholar 

  26. Ruan SG, Filfil RS (2004) Dynamics of a two-neuron system with discrete and distributed delays. Physica D 191(3–4): 323–342

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. Xiong WJ, Cao JD (2005) Absolutely exponential stability of Cohen–Grossberg neural networks with unbounded delays. Neurocomputing 68: 1–12

    Article  Google Scholar 

  28. Wang ZD, Liu YR, Fraser K, Liu XH (2006) Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays. Phys Lett A 345(4): 288–297

    Article  ADS  Google Scholar 

  29. Wang ZD, Liu YR, Li M, Liu XH (2006) Stability analysis for stochastic Cohen–Grossberg neural networks with mixed time delays. IEEE Trans Neural Netw 17(3): 814–820

    Article  Google Scholar 

  30. Sun CY, Feng CB (2003) Global robust exponential stability of interval neural networks with delay. Neural Process Lett 17(1): 107–115

    Article  Google Scholar 

  31. Sun CY, Feng CB (2004) On robust exponential periodicity of interval neural networks with delays. Neural Process Lett 20(1): 53–61

    Article  Google Scholar 

  32. Ding K, Huang NJ (2006) Global robust exponential stability of interval general BAM neural network with delays. Neural Process Lett 23(2): 171–182

    Article  Google Scholar 

  33. Ding K, Huang NJ, Xu X (2007) Global robust exponential stability of interval BAM neural network with mixed delays under uncertainty. Neural Process Lett 25(2): 127–141

    Article  Google Scholar 

  34. Xu SY, Lam J, Ho DWC (2005) Novel global robust stability criteria for interval neural networks with multiple time-varying delays. Phys Lett A 342(4): 322–330

    Article  ADS  Google Scholar 

  35. Arik S (2003) Global robust stability of delayed neural networks. IEEE Trans Circuit Syst I 50(1): 156–160

    Article  MathSciNet  Google Scholar 

  36. Cao JD, Wang J (2005) Global asymptotic and robust stability of recurrent neural networks with time delays. IEEE Trans Circuit Syst I 52(2): 417–426

    Article  MathSciNet  Google Scholar 

  37. Singh V (2005) Global robust stability of delayed neural networks: an LMI approach. IEEE Trans Circuit Syst II 52(1): 33–36

    Article  Google Scholar 

  38. Li CD, Liao XF, Zhang R (2004) Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach. Phys Lett A 328(6): 452–462

    Article  ADS  MathSciNet  Google Scholar 

  39. Rong LB, Chen TP (2006) New results on the robust stability of Cohen–Grossberg neural networks with delays. Neural Process Lett 24(3): 193–202

    Article  Google Scholar 

  40. Forti M, Tesi A (1995) New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Trans Circuit Syst I 42(7): 354–366

    Article  MATH  MathSciNet  Google Scholar 

  41. Cao JD, Wang J (2005) Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans Circuit Syst I 52(5): 920–931

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jin-De Cao.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Song, QK., Cao, JD. Robust Stability in Cohen–Grossberg Neural Network with both Time-Varying and Distributed Delays. Neural Process Lett 27, 179–196 (2008). https://doi.org/10.1007/s11063-007-9068-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-007-9068-3

Keywords

Mathematics Subject Classification (2000)

Navigation