Skip to main content

Advertisement

SpringerLink
Log in

Stochastic robust stability for neutral-type impulsive interval neural networks with distributed time-varying delays

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

This paper studies the stochastic robust stability for impulsive interval neural networks with distributed time-varying delays of neutral type. The present model is a more general description of the real world in nature, where both discrete delays and distributed delays are taken into consideration. The parameter uncertainties are assumed to be bounded and laid in a certain interval. By constructing a novel Lyapunov–Krasovskii functional, together with some inequality techniques and stochastic stability theory, some sufficient criteria are driven in terms of linear matrix inequalities (LMI), which are easily to verify and can be solved by MATLAB. Furthermore, the results obtained in this paper are less conservative and cover more situations compared with the ones published in the literature.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. Haykin S (1994) Neural networks: a comprehensive foundation. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  2. Hopfield JJ (1984) Neuron with graded response have collective computational properties like those of two-state neurons. Proc Nat Acad Sci 81(5):3088–3092. doi:10.1073/pnas.81.10.3088

    Article  Google Scholar 

  3. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci 79(8):2554–2558

    Article  MathSciNet  Google Scholar 

  4. Juang JC (1999) Stability analysis of Hopfield-type neural networks. IEEE Trans Neural Netw 10(6):1366–1374. doi:10.1109/72.809081

    Article  MathSciNet  Google Scholar 

  5. Li XL (2008) Exponential robust stability of stochastic interval Hopfield neural networks with time-varying delays. In: Proceedings of the 27th Chinese control conference, pp 701–704. doi: 10.1109/CHICC.2008.4605578

  6. Forti M, Nistri P (2003) On global stability of Hopfield neural networks with discontinuous neuron activations. In: Proceedings of the 2003 international symposium on circuits and systems, pp 478-481. doi:10.1109/ISCAS.2003.1205060

  7. Huang H, Ho DWC, Lam J (2005) Stochastic stability analysis of fuzzy Hopfield neural networks with time-varying delays. IEEE Trans Circuits Syst 52(5):251–255. doi:10.1109/TCSII.2005.846305

    Article  Google Scholar 

  8. Zhang QL, Jia GJ (2007) Impulsive synchronization of typical Hopfield neural networks. In: Proceedings of the 26th Chinese control conference, pp 270–273. doi:10.1109/CHICC.2006.4346890

  9. Zhang K, Lian J, Sun XM, Wang D (2010) Stability of switched Hopfield neural networks with time-varying delay. American control conference, pp 4943–4948

  10. Chua LO, Yang L (1988) Cellular neural networks: theory. IEEE Trans Circuits Syst 35(10):1257–1272. doi:10.1109/31.7600

    Article  MathSciNet  MATH  Google Scholar 

  11. Baldi P, Atiya AF (1994) How delays affect neural dynamics and learning. IEEE Trans Neural Netw 5(4):612–621. doi:10.1109/72.298231

    Article  Google Scholar 

  12. Li CD, Liao XF, Zhang R (2004) Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach. Physics Lett A 328(6):452–462. doi:10.1016/j.physleta.2004.06.053

    Article  MathSciNet  MATH  Google Scholar 

  13. Bainov DD, Simeonov PS (1989) Systems with impulse effect: stability, theory and applications. Ellis Horwood, Chichester

    MATH  Google Scholar 

  14. Stamova IM (2009) Stability analysis of impulsive functional differential equations. Walter de Gruyter, Berlin

    Book  MATH  Google Scholar 

  15. Stamova IM, Ilarionov R (2010) On global exponential stability for impulsive cellular neural networks with time-varying delays. Comput Math Appl 59(11):3508–3515. doi:10.1016/j.camwa.2010.03.043

    Article  MathSciNet  MATH  Google Scholar 

  16. Liu B (2008) Stability of solutions of stochastic impulsive systems via comparison approach. IEEE Trans Automat Control 53(9):2128–2133. doi:10.1109/TAC.2008.930185

    Article  MathSciNet  Google Scholar 

  17. Li CX, Sun JT, Sun RY (2010) Stability analysis of a class of stochastic differential delay equations with nonlinear impulsive effects. J Franklin Inst 347(7):1186–1198. doi:10.1016/j.jfranklin.2010.04.017

    Article  MathSciNet  MATH  Google Scholar 

  18. Zhang H, Guan ZH, Feng G (2008) Reliable dissipative control for stochastic impulsive systems. Automatica 44(4):1004–1010. doi:10.1016/j.automatica.2007.08.018

    Article  MathSciNet  Google Scholar 

  19. Zhang HG, Dong M, Wang YC, Sun N (2010) Stochastic stability analysis of neutral-type impulsive neural networks with mixed time-varying delays and Markovian jumping. Neurocomputing 73(13–15). doi:10.1016/j.neucom.2010.04.016

  20. Balasubramaniam P, Lakshmanan S, Rakkiyappan R (2009) Delay-interval dependent robust stability criteria for stochastic neural networks with linear fractional uncertainties. Neurocomputing 72(16–18):3675–3682. doi:10.1016/j.neucom.2009.06.006

    Article  Google Scholar 

  21. Morita M (1993) Associative memory with nonmonotone dynamics. Neural Netw 6(1):115–126. doi:10.1016/S0893-6080(05)80076-0

    Article  Google Scholar 

  22. Yoshizawa S, Morita M, Amari S (1993) Capacity of associative memory using a nonmonotonic neuron model. Neural Netw 6(2):167–176. doi:10.1016/0893-6080(93)90014-N

    Article  Google Scholar 

  23. Bernt K (2003) Stochastic differential equations: an introduction with applications. Springer, New York

    MATH  Google Scholar 

  24. Sanchez EN, Perez JP (1997) Input-to-state stability (ISS) analysis for dynamic neural networks. Int Conf Neural Netw 2:1139–1143. doi:10.1109/ICNN.1997.616191

    Google Scholar 

  25. Gu K (2000) An integral inequality in the stability problem of time-delay systems. In: Proceedings of 39th IEEE conference on decision and control, vol 3, pp 2805–2810. doi:10.1109/CDC.2000.914233

  26. Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM Studies in Applied Mathematics, SIAM, Philadelphia

    Book  MATH  Google Scholar 

  27. Huang LR, Mao XR (2009) Delay-dependent exponential stability of neutral, stochastic delay systems. IEEE Trans Automat Control 54(1):147–152. doi:10.1109/TAC.2008.2007178

    Article  MathSciNet  Google Scholar 

  28. Zhang Y, He Y, Wu M (2009) Delay-dependent robust stability for uncertain, stochastic systems with interval time-varying delay. Acta Automatica Sinica 35(5):577–582. doi:10.1016/S1874-1029(08)60088-9

    MathSciNet  MATH  Google Scholar 

  29. Li XD (2010) Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type. Appl Math Comput 215(12):4370–4384. doi:10.1016/j.amc.2009.12.068

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was partially supported by the Fundamental Research Funds for the Central Universities of China (Project No. CDJXS11180011 and CDJZR10185501) and the National Natural Science Foundation of China (Grant No. 60974020).

Author information

Authors and Affiliations

  1. State Key Laboratory of Power Transmission Equipment & System Security and New Technology, College of Computer, Chongqing University, 400044, Chongqing, China

    Wenfeng Hu, Chuandong Li & Sichao Wu

Authors
  1. Wenfeng Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chuandong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sichao Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chuandong Li.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hu, W., Li, C. & Wu, S. Stochastic robust stability for neutral-type impulsive interval neural networks with distributed time-varying delays. Neural Comput & Applic 21, 1947–1960 (2012). https://doi.org/10.1007/s00521-011-0598-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-011-0598-2

Keywords

Search

Navigation