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Stability Criterion of Discrete-Time Recurrent Neural Networks with Periodic Delays

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Neural Information Processing (ICONIP 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7064))

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Abstract

This paper deals with the problem of stability criterion of discrete-time recurrent neural networks with periodic delays. It is written as a discrete-time multi-switched liner system (DMSLS), applying the parameter and time dependent Lyapunov functions we obtain several new sufficient conditions and sufficient conditions for asymptotically stability of these systems.

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References

  1. Cao, J.D., Yuan, K., Li, H.X.: Global asymptotical stability of recurrent neural networks with multiple discrete delays and distributed delays. IEEE Trans. Neural Netw. 17(6), 1646–1651 (2006)

    Article  Google Scholar 

  2. Li, T., Guo, L., Sun, C., Lin, C.: Further Results on Delay-Dependent Stability Criteria of Neural Networks With Time-Varying Delays. IEEE Trans. on Neural Networks 19(4), 726–730 (2008)

    Article  Google Scholar 

  3. Huang, H., Feng, G., Cao, J.D.: Robust state estimation for uncertain neural networks with time-varying delay. IEEE Trans. on Neural networks 19(8), 1329–1339 (2008)

    Article  Google Scholar 

  4. Xiang, H., Yan, K.M., Wang, B.Y.: Existence and global exponential stability of periodic solution for delayed discrete high-order Hopfield-type neural networks. Physics Letters A 352, 341–349 (2006)

    Article  MATH  Google Scholar 

  5. Xiang, H., Yan, K.M., Wang, B.Y.: Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks. Discrete Dynamics in Nature and Society 2005(3), 281–297 (2005)

    Article  MATH  Google Scholar 

  6. Huang, C.X., He, Y.G., Huang, L.H., Lai, M.Y.: Global exponential periodicity of three-unit neural networks in a ring with time-varying delays. Neurocomputing 71, 1595–1603 (2008)

    Article  Google Scholar 

  7. Jiang, H., Cao, J.D.: Global exponential stability of periodic neural networks with time-varying delays. Neurocomputing 70, 343–350 (2006)

    Article  Google Scholar 

  8. Shao, Y., Dai, B.: The existence of exponential periodic attractor of impulsive BAM neural network with periodic coefficients and distributed delays. Neurocomputing 73, 3123–3131 (2010)

    Article  Google Scholar 

  9. Liu, Y., You, Z., Cao, L.: On the almost periodic solution of generalized Hopfield neural networks with time-varying delays. Neurocomputing 69, 1760–1767 (2006)

    Article  Google Scholar 

  10. Liu, B., Huang, L.: Existence and exponential stability of almost periodic solutions for Hopfield neural networks with delays. Neurocomputing 68, 196–207 (2005)

    Article  Google Scholar 

  11. Cao, J.D., Wang, J.: Global Exponential Stability and Periodicity of Recurrent Neural Networks With Time Delays. IEEE Trans. on circuits and syst. I 52, 920–931 (2005)

    Article  Google Scholar 

  12. Lou, X., Cui, B.: Delay-Dependent Criteria for Global Robust Periodicity of Uncertain Switched Recurrent Neural Networks With Time-Varying Delay. IEEE Trans. on Neural Networks 19, 549–557 (2008)

    Article  Google Scholar 

  13. Huang, Z., Wang, X., Feng, C.: Multiperiodicity of Periodically Oscillated Discrete-Time Neural Networks with Transient Excitatory Self-Connections and Sigmoidal Nonlinearities. IEEE Trans. on Neural Networks 21, 1643–1655 (2010)

    Article  Google Scholar 

  14. Allegretto, W., Papini, D., Forti, M.: Common Asymptotic Behavior of Solutions and Almost Periodicity for Discontinuous, Delayed, and Impulsive Neural Networks. IEEE Trans. on Neural Networks 21, 1110–1125 (2010)

    Article  Google Scholar 

  15. Zhang, L., Zhang, Y., Yu, J.: Multiperiodicity and Attractivity of Delayed Recurrent Neural Networks With Unsaturating Piecewise Linear Transfer Functions. IEEE Trans. on Neural Networks 19, 158–167 (2008)

    Article  Google Scholar 

  16. Chen, B., Wang, J.: Global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays. IEEE Trans. on Neural Networks 16(6), 1440–1449 (2005)

    Article  Google Scholar 

  17. Wu, X.R., Wang, Y.N., Huang, L.H., Zuo, Y.: Robust exponential stability criterion for uncertain neural network swith discontinuous activation functions and time-varying delay. Neurocomputing 73, 1265–1271 (2010)

    Article  Google Scholar 

  18. Song, Q., Cao, J.D.: Global Dissipativity on Uncertain Discrete-Time Neural Networks with Time-Varying Delays. Discrete Dynamics in Nature and Society (2010), Article ID 810408, 19 pages (2010)

    Google Scholar 

  19. Arzen, K.E., Bicchi, A., Hailes, S., Johansson, K.H., Lygeros, J.: On the design and control of wireless networked embedded systems. In: Proceedings of the 2006 IEEE Computer Aided Control Systems Design Symposium, Munich, Germany (2006)

    Google Scholar 

  20. Hetel, L., Daafouz, J., Iung, C.: Equivalence between the LyapunovCKrasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems. Nonlinear Analysis: Hybrid Systems 2, 697–705 (2008)

    MATH  Google Scholar 

  21. Xu, J., Cao, Y., Sun, Y., Tang, J.: Absolute Exponential Stability of Recurrent Neural Networks With Generalized Activation Function. IEEE Trans. on Neural Networks 19(6), 1075–1089 (2008)

    Article  Google Scholar 

  22. Daafouz, J., Riedinger, P., Iung, C.: Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Trans. on Automatic Control 47(11), 1883–1887 (2002)

    Article  Google Scholar 

  23. Li, J., Diao, Y.F., Li, M.D., Yin, X.: Stability analysis of Discrete Hopfield Neural Networks with the nonnegative definite monotone increasing weight function matrix. Discrete Dynamics in Nature and Society 2009,Article ID 673548, 10 (2009)

    MATH  Google Scholar 

  24. Li, J., Diao, Y., Mao, J., Zhang, Y., Yin, X.: Stability Analysis of Discrete Hopfield Neural Networks with Weight Function Matrix. In: Kang, L., Cai, Z., Yan, X., Liu, Y. (eds.) ISICA 2008. LNCS, vol. 5370, pp. 760–768. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  25. Li, J., Wu, W.G., Yuan, J.M., Tan, Q.R., Yin, X.: Delay-dependent stability criterion of arbitrary switched linear systems with time-varying delay. Discrete Dynamics in Nature and Society 2010, Article ID 347129, 16 (2010)

    MATH  Google Scholar 

  26. Li, J., Yang, J., Wu, W.G.: Stability analysis of discrete Hopfield neural networks with column arbitrary-dominant weight matrix. Neurocomputing (revised manuscript submitted to, 2011)

    Google Scholar 

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Yin, X., Wu, W., Tan, Q. (2011). Stability Criterion of Discrete-Time Recurrent Neural Networks with Periodic Delays. In: Lu, BL., Zhang, L., Kwok, J. (eds) Neural Information Processing. ICONIP 2011. Lecture Notes in Computer Science, vol 7064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24965-5_33

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  • DOI: https://doi.org/10.1007/978-3-642-24965-5_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24964-8

  • Online ISBN: 978-3-642-24965-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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