Advertisement

A New Approach in Stability Analysis of Hopfield-Type Neural Networks: Almost Stability

  • Kaiming Wang
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 311)

Abstract

In this paper,we presented a new stability concept for neural networks: almost stability. The necessary and sufficient conditions of almost stability of the Hopfield-type neural networks were proposed. Examples were also given to our conditions.

Keywords

almost stability Hopfield neural network almost positive definite 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Liu, Y., Wang, Z., Liu, X.: Asymptotic stability for neural networks with mixed time-delays: The discrete-time case. Neural Networks 22, 67–74 (2009)CrossRefGoogle Scholar
  2. 2.
    Zhang, X.-M., Han, Q.-L.: New Lyapunov-Krasovski functionals for global asymptotic stability of delayed neural networks. IEEE T. Automat. Contr. 20(2), 533–539 (2009)Google Scholar
  3. 3.
    Qiao, H., Peng, J., Xu, Z.: Nonlinear measures: a new approach to exponential stability analysis for Hopfield-type neural networks. IEEE T. Neural Networ. 12(2), 360–370 (2001)CrossRefGoogle Scholar
  4. 4.
    Mak, K.L., Peng, J.G., Xu, Z.B., Yiu, K.F.C.: A new stability criterion for discrete-time neural networks: Noniear spectral radius. Chaos Soliton Fract. 31, 424-436-1190 (2007)Google Scholar
  5. 5.
    Rantzer, A.: A dual to Lyapunov’s stability theorem. Syst. Control Lett. 42(3), 161–168 (2001)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Prajna, S., Parrilo, P.A., Rantzer, A.: Nonlinear control synthesis by convex optimization, IEEE T. Automat. Contr. 49(2), 117–128 (2004)MathSciNetGoogle Scholar
  7. 7.
    Vaidya, U., Mehta, P.G.: Lyapunov measure for almost everywhere stability. IEEE T. Automat. Contr. 30(1), 307–323 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Monzon, P., Potrje, R.: Local implication of almost global stability. Dynam. Syst. 24(1), 109–115 (2009)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kaiming Wang
    • 1
    • 2
  1. 1.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anChina
  2. 2.School of ScienceChang’an UniversityXi’anChina

Personalised recommendations