Impulsive Robust Control of Interval Hopfield Neural Networks

  • Yinping Zhang
  • Jitao Sun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3496)

Abstract

This paper discusses impulsive control and synchronization of interval Hopfield neural networks (HNN for short). Based on the matrix measure and new comparison theorem, this paper presents an impulsive robust control scheme of the interval HNN. We derive some sufficient conditions for the stabilization and synchronization of interval Hopfield neural networks via impulsive control with varying impulsive intervals. Moreover, the large upper bound of impulsive intervals for the stabilization and synchronization of interval HNN can be obtained.

Keywords

Drive System Matrix Measure Lorenz System Impulsive Control Hopfield Neural Network 
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.

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References

  1. 1.
    Hopfield, J.J.: Neural Networks and Physical Systems with Emergent Collective Computational Abilities. Proc. Nate. Acad. 9, 2554–2558 (1982)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Hopfield, J.J.: Neurons with Graded Response Have Collective Computational Properties Like Those of Two-State Neurons. Proc. Nate. Acad. 81, 3088–3092 (1984)CrossRefGoogle Scholar
  3. 3.
    Hopfield, J.J., Tank, D.: Neural Computation of Decisions Optimization Problems. Biolcyhem 52, 141–152 (1985)MATHMathSciNetGoogle Scholar
  4. 4.
    Guan, Z.H., Lam, J., Chen, G.R.: On Impulsive Autoassociative Neural Networks. Networks 13, 63–69 (2000)Google Scholar
  5. 5.
    Guan, Z.H., Chen, G.R., Qin, Y.: On Equilibria, Stability, and Instability of Hopfield Neural Networks. IEEE Trans. on Neural Networks 11, 534–540 (2000)CrossRefGoogle Scholar
  6. 6.
    Liu, B., Liu, X.Z., Liao, X.X.: Robust H-stability for Hopfield Neural Networks with Impulsive Effects. In: Proceeding of Dynamics of Continuous, Discrete and Impulsive Systems, vol. 1 (2003)Google Scholar
  7. 7.
    Liao, X.X.: Stability of Hopfield-type Neural Networks (1). Science in China (A) 38, 407–418 (1995)MATHGoogle Scholar
  8. 8.
    Liao, X.X., Liao, Y.: Stability of Hopfield-type Neural Networks (2). Science in China (A) 40, 813–816 (1997)MATHCrossRefGoogle Scholar
  9. 9.
    Fang, Y., Kincaid, T.G.: Stability Analysis of Dynamical Neural Networks. IEEE Trans. Neural Networks 7, 996–1006 (1996)CrossRefGoogle Scholar
  10. 10.
    Liang, X.B., Wu, L.D.: New Sufficient Conditions for Absolute Stability of Neural Networks. IEEE Trans. Circuits Syst. 45, 584–586 (1998)MATHMathSciNetGoogle Scholar
  11. 11.
    Bainov, D., Simeonov, P.S.: Systems With Impulse Effect: Stability, Theory and Applications. Halsted Press, New York (1989)MATHGoogle Scholar
  12. 12.
    Lakshmikantham, V., Bainov, D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)MATHGoogle Scholar
  13. 13.
    Yang, T.: Impulsive Control. IEEE Trans. Autom. Control 44, 1081–1083 (1999)MATHCrossRefGoogle Scholar
  14. 14.
    Yang, T.: Impulsive Systems and Control: Theory and Applications, September 2001. Nova Science Publishers, Inc., Huntington (2001)Google Scholar
  15. 15.
    Li, Z.G., Wen, C.Y., Soh, Y.C.: Analysis and Design of Impulsive Control Systems. IEEE Trans. Autom. Control 46, 894–897 (2001)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Sun, J.T., Zhang, Y.P.: Impulsive Control of a Nuclear Spin Generator. J. of Computational and Applied Mathematics 157, 235–242 (2003)MATHCrossRefGoogle Scholar
  17. 17.
    Xie, W., Wen, C.Y., Li, Z.G.: Impulsive Control for the Stabilization and Synchronization of Lorenz Systems. Phys. Lett. A 275, 67–72 (2000)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Yang, T.: Impulsive Control Theory. Springer, Berlin (2001)MATHGoogle Scholar
  19. 19.
    Sun, J.T., Zhang, Y.P., Wu, Q.D.: Less Conservative Conditions for Asymptotic Stability of Impulsive Control Systems. IEEE Trans. Autom. Control. 48, 829–831 (2003)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Sun, J.T., Zhang, Y.P., Wu, Q.D.: Impulsive Control for the Stabilization and Synchronization of Lorenz Systems. Physics Letter A. 298, 153–160 (2002)MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Ambrosetti, A., Prodi, G.: A primer of Nonlinear Analysis. Cambridge University, New York (1993)Google Scholar
  22. 22.
    Sun, J.T., Zhang, Y.P.: Some Simple Global Synchronization Criterions for Coupled Time-varying Chaotic Systems. Chaos, Solitons & Fractals 19, 93–98 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yinping Zhang
    • 1
  • Jitao Sun
    • 1
  1. 1.Dept. of Applied MathematicsTongji UniversityShanghaiChina

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