Advertisement

Robust Stability in Interval Delayed Neural Networks of Neutral Type

  • Jianlong Qiu
  • Qingjun Ren
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4113)

Abstract

In this paper, the problem of global robust stability (GRAS) is investigated for a class of interval neural networks described by nonlinear delayed differential equations of the neutral type. A sufficient criterion is derived by an approach combining the Lyapunov-Krasovskii functional with the linear matrix inequality (LMI). Finally, the effectiveness of the present results is demonstrated by a numerical example.

Keywords

Linear Matrix Inequality Robust Stability Recurrent Neural Network Cellular Neural Network Global Asymptotic Stability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cao, J., Wang, J.: Global Exponential Stability and Periodicity of Recurrent Neural Networks with Time Delays. IEEE Trans. Circuits Syst. I 52(5), 925–931 (2005)MathSciNetGoogle Scholar
  2. 2.
    Cao, J., Wang, J.: Global Asymptotic Stability of a General Class of Recurrent Neural Networks with Time-varying Delays. IEEE Trans. Circuits Syst. I 50(1), 34–44 (2003)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Cao, J., Ho, D.W.C.: A General Framework for Global Asymptotic Stability Analysis of Delayed Neural Networks Based on LMI Approach. Chaos, Solitons and Fractals 24(5), 1317–1329 (2005)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Boyd, S., Ghaoui, L.E.I., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia (1994)MATHGoogle Scholar
  5. 5.
    Xu, S., Lam, J., Ho, D.W.C., Zou, Y.: Delay-dependent Exponential Stability for a Class of Neural Networks with Time Delays. J. Comput. Appl. Math. 183, 16–28 (2005)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Jiang, H., Teng, Z.: Global Exponential Stability of Cellular Neural Networks with Time-varying Coefficients and Delays. Neural Networks 17, 1415–1425 (2004)MATHCrossRefGoogle Scholar
  7. 7.
    Liao, X.F., Wang, J.: Global and Robust Stability of Interval Hopfield Neural Networks with Time-varying Delays. Int. J. Neural Syst. 13(2) (2003)Google Scholar
  8. 8.
    Cao, J., Chen, T.: Globally Exponentially Robust Stability and Periodicity of Delayed Neural Networks. Chaos, Solitons and Fractals 22(4), 957–963 (2004)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Cao, J., Huang, D., Qu, Y.: Global Robust Stability of Delayed Recurrent Neural Networks. Chaos, Solitons and Fractals 23, 221–229 (2005)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Cao, J., Li, H., Lei, H.: Novel Results Concerning Global Robust Stability of Delayed Neural Networks. Nonlinear Analysis, Series B 7(3), 458–469 (2006)MATHGoogle Scholar
  11. 11.
    Li, D.: Matrix Theory and Its Applications. Chongqing University Press, Chongqing (1988)Google Scholar
  12. 12.
    Cao, J., Li, X.: Stability in Delayed Cohen-Grossberg Neural Networks: LMI Optimization Approach. Physica D: Nonlinear Phenomena 212(1-2), 54–65 (2005)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Cao, J., Li, P., Wang, W.: Global Synchronization in Arrays of Delayed Neural Networks with Constant and Delayed Coupling. Physics Letters A 353(4), 318–325 (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jianlong Qiu
    • 1
    • 2
  • Qingjun Ren
    • 2
  1. 1.Department of MathematicsSoutheast UniversityNanjingChina
  2. 2.Department of MathematicsLinyi Normal UniversityLinyiChina

Personalised recommendations