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On Robust Exponential Periodicity of Interval Neural Networks with Delays

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Abstract

In this Letter, based on globally Lipschitz continous activation functions, new conditions ensuring existence, uniqueness and global robust exponential stability of the periodic solution of interval-delayed neural networks with periodic input are obtained. All the results obtained are generalizations of some resent results reported in the literature for neural networks with constant input.

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References

  1. Arik, S.: Global robust stability of delayed neural networks, IEEE Transaction on Circuits Systems. I, 50(1) (2003), 156–160.

    Google Scholar 

  2. Bouzerman, A. and Pattison, T.: Neural network for quadratic optimization with bound constraints, IEEE Transactions on Neural Networks, 4 (1993), 293–303.

    Google Scholar 

  3. Cao, J.: On stability of delayed cellular neural networks, Physics Letters A, 261 (1999), 303–308.

    Google Scholar 

  4. Cao, J. and Wang, L.: Exponential stability and periodic oscillatory solution in BAM networks with delays, IEEE Transactions on Neural Networks, 13(2) (2002), 457–463.

    Google Scholar 

  5. Cao, J. and Zhou, D.: Stability analysis of delayed cellular neural networks, Neural Networks, 11 (1998), 1601–1605.

    Google Scholar 

  6. Chen, T.: Convergence of delayed dynamical systems. Neural Processing Letters, 10 (1999), 267–271.

    Google Scholar 

  7. Feng, C. and Plamondon, R.: On the stability analysis of delayed cellular neural networks, Neural Networks, 14 (2001), 1181–1188.

    Google Scholar 

  8. Forti, M.: On global asymptotic stability of a class of nonlinear systems arising in neural network theory, Journal of Differential Equations, 113 (1994), 246–264.

    Google Scholar 

  9. Forti, M. and Tesi, A.: New conditions for global stability of neural networks with application to linear and quadratic programming Problems, IEEE Transactions on Circuits and Systems I, 42 (1995), 354–366.

    Google Scholar 

  10. Gopalsamy, K. and He, X. Z.: Delay-independent stability in bi-directional associative memory networks, IEEE Transactions on Neural Networks, 5 (1994), 998–1002.

    Google Scholar 

  11. Hopfield, J.: Neurons with graded response have collective computation properties like those of two-state neurons, Proceedings of the National Academic Science, 81 (1984), 3088–3092.

    Google Scholar 

  12. Huang, H., Cao, J. and Wang, J.: Global exponential stability and periodic solutions of recurrent neural networks with delays, Physics Letter A, 298 (2002), 393–404.

    Google Scholar 

  13. Liao, X. and Yu, J.: Robust stability for interval Hopfield neural networks with time delay, IEEE Transactions on Neural Networks, 9 (1998), 1042–1045.

    Google Scholar 

  14. Liao, X. et al.: Novel robust stability criteria for interval-delayed Hopfield neural networks, IEEE Transactions on Circuits and Systems: I, 48(11) (2001), 1355–1358.

    Google Scholar 

  15. Mohamad, S. and Gopalsamy, K.: Exponential stability of continuous-time and discretetime cellular neural networks with delays, Applied Mathematics and Computation, 135 (2003), 17–38.

    Google Scholar 

  16. Morita, M.: Associative memory with non-monntone dynamics, Neural Networks, 6 (1993), 115–126.

    Google Scholar 

  17. Sudharsanan, S. and Sundareshan, M.: Exponential stability and a systematic synthesis of a neural network for quadratic minimization, Neural Networks, 4 (1991), 599–613.

    Google Scholar 

  18. Sun, C., Fei, S., Zhang, K., Cao, J. and Feng, C.: On absolute exponential stability of a class of neural networks, Proceedings of the 15th International Federation of Automatic Control (IFAC'02), July 21-26, 2002, Barcelona, Spain.

  19. Sun, C. and Feng, C.: On exponential stability of delayed neural networks with globally Lipschitz continuous activation functions, Proceedings of the 4th World Congress on Intelligent Control and Automation, Shanghai, Vol. 3, June 2002, pp. 1953–1957.

  20. Sun, C., and Feng. C.: Global robust exponential stability of interval neural networks with delays, Neural Processing Letters, 17(1) (2003), 107–115.

    Google Scholar 

  21. Sun, C. and Feng, C.: On exponential periodicity of delayed neural networks, Proceedings of the 2003 IEEE International Symposium on Circuits and Systems : 681-684, May 25-28, 2003, Thailand.

  22. Sun, C. and Feng, C.: Exponential periodicity of continuous-time and discrete-time neural networks with delays. Neural Processing Letters, 19(2) (2004), 131–146.

    Google Scholar 

  23. Sun, C. and Liu, D. and Feng, C.: New results on exponential periodicity of delayed neural networks, Proceedings of the 2003 IEEE Joint Conference on Neural Networks: 902-907, July 20-24, USA.

  24. Sun, C., Zhang, K., Fei, S. and Feng, C.: On exponential stability of delayed neural networks with a general class of activation functions, Physics Letters A, 298(2/3) (2002), 122–132.

    Google Scholar 

  25. Tank, D. and Hopfield, J.: Simple neural optimization networks: An A/D converter, signal decision circuits and a linear programming circuit, IEEE Transactions on Circuits and Systems, 33 (1987), 533–541.

    Google Scholar 

  26. Yoshizawa, S., Morita, M. and Amari, S. Capacity of associative memory using a nonmonotonic neural model, Neural Networks, 6 (1993), 167–176.

    Google Scholar 

  27. Zhang, Y., Pheng, H. A. and Vadakkepat, P.: Absolute periodicity and absolute stability of delayed neural networks, IEEE Transactions on Circuits and Systems: I, 49 256–261, 2002.

    Google Scholar 

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Sun, C., Feng, CB. On Robust Exponential Periodicity of Interval Neural Networks with Delays. Neural Processing Letters 20, 53–61 (2004). https://doi.org/10.1023/B:NEPL.0000039426.58277.7e

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  • DOI: https://doi.org/10.1023/B:NEPL.0000039426.58277.7e

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