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Stability Analysis of Neutral Neural Networks with Time Delay

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Advances in Neural Networks - ISNN 2006 (ISNN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3971))

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Abstract

A method is proposed for asymptotic stability analysis of neutral neural networks with delayed state. The delay is assumed unknown, but constant. Sufficient conditions on delay-independent asymptotic stability are given in terms of the existence of symmetric and positive definite solutions of a constant Riccati algebraic matrix equation coupled with a discrete Lyapunov equation.

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References

  1. Cao, J.D., Li, Q.: On the exponential stability and periodic solution of delayed cellular neural networks. J. Math. Anal. and Appl. 252(1), 50–64 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Curt, W.: Reactive Molecules: The Neutral Reactive Intermediates in Organic Chemistry. Wilay Press, New York (1984)

    Google Scholar 

  3. Fu, C.J., He, H.L., Liao, X.X.: Globally Stable Periodic State of Delayed Cohn-Grossberg Neural Networks. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 276–281. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  4. Hale, J.K., Verduyn Lunel, S.M.: Introduation to Functional Differential Equations. In: Applied Math. Sciences, vol. 99. Springer, New York (1991)

    Google Scholar 

  5. He, H.L., Wang, Z.S., Liao, X.X.: Stability Analysis of Uncertain Neural Networks with Linear and Nonlinear Time Delays. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 199–202. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Liao, X.X., Xiao, D.M.: Globally Exponential Stability of Hopfield Neural Networks with Time-varying Delays. ACTA Electronica Sinica 28(1), 87–90 (2000)

    Google Scholar 

  7. Liao, X.X., Wang, J.: Algebraic Criteria for Global Exponential Stability of Cellular Neural Networks with Multiple Time Delays. IEEE Trans. Circuits and Systems I. 50(2), 268–275 (2003)

    Article  MathSciNet  Google Scholar 

  8. Shen, Y., Zhao, G.Y., Jiang, M.H., Mao, X.R.: Stochastic Lotka-Volterra Competitive Systems with Variable Delay. In: Huang, D.-S., Zhang, X.-P., Huang, G.-B. (eds.) ICIC 2005. LNCS, vol. 3645, pp. 238–247. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Shen, Y., Zhao, G.Y., Jiang, M.H., Hu, S.G.: Stochastic High-order Hopfield Neural Networks. In: Wang, L., Chen, K., S. Ong, Y. (eds.) ICNC 2005. LNCS, vol. 3610, pp. 740–749. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  10. Zeng, Z.G., Wang, J., Liao, X.X.: Global Exponential Stability of A General Class of Recurrent Neural Networks with Time-varying Delays. IEEE Trans. Circuits and Syst. I 50(10), 1353–1358 (2003)

    Article  MathSciNet  Google Scholar 

  11. Zeng, Z.G., Wang, J., Liao, X.X.: Stability Analysis of Delayed Cellular Neural Networks Described Using Cloning Templates. IEEE Trans. Circuits and Syst. I 51(11), 2313–2324 (2004)

    Article  MathSciNet  Google Scholar 

  12. Shen, Y., Jiang, M.H., Liao, X.X.: Global Exponential Stability of Cohen-Grossberg Neural Networks with Time-varying Delays and Continuously Distributed Delays. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 156–161. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Zhang, Y.M., Guo, L., Wu, L.Y., et al.: On Stochastic Neutral Neural Networks. In: Wang, J., Liao, X.-F., Yi, Z. (eds.) ISNN 2005. LNCS, vol. 3496, pp. 69–74. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Zhang, Y.M., Shen, Y., Liao, X.X.: Exponential for Stochastic Interval Delayed Hopfield Neural Networks. Control Theory and Applications 20(12), 1299–1300 (2003)

    Google Scholar 

  15. Wang, Z.S., He, H.L., Liao, X.X.: Stability Analysis of Uncertain Neural Networks with Delay. In: Yin, F.-L., Wang, J., Guo, C. (eds.) ISNN 2004. LNCS, vol. 3173, pp. 44–48. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

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He, H., Liao, X. (2006). Stability Analysis of Neutral Neural Networks with Time Delay. In: Wang, J., Yi, Z., Zurada, J.M., Lu, BL., Yin, H. (eds) Advances in Neural Networks - ISNN 2006. ISNN 2006. Lecture Notes in Computer Science, vol 3971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11759966_22

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  • DOI: https://doi.org/10.1007/11759966_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34439-1

  • Online ISBN: 978-3-540-34440-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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