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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 372324, 12 pages
http://dx.doi.org/10.1155/2012/372324
Research Article

Input-to-State Stability for Dynamical Neural Networks with Time-Varying Delays

Department of Mathematics, Chongqing Normal University, Chongqing 400047, China

Received 22 August 2012; Revised 22 December 2012; Accepted 22 December 2012

Academic Editor: Sabri Arik

Copyright © 2012 Weisong Zhou and Zhichun Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. J. Hopfield, “Neurons with graded response have collective computational properties like those of two state neurons,” Proceeding of the National Academy of Sciences of the United States of America, vol. 81, no. 10, pp. 3088–3092, 1984. View at Publisher · View at Google Scholar
  2. S. Arik, “Stability analysis of delayed neural networks,” IEEE Transactions on Circuits and Systems I, vol. 47, no. 7, pp. 1089–1092, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. T. Ensari and S. Arik, “Global stability analysis of neural networks with multiple time varying delays,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1781–1785, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  4. C. K. Ahn, “Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay,” Information Sciences, vol. 180, pp. 4582–4594, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. C. K. Ahn, “2 filtering for time-delayed switched Hopfield neural networks,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 5, pp. 1831–1843, 2011.
  6. T. W. Huang, A. Chan, Y. Huang, and J. D. Cao, “Stability of Cohen-Grossberg neural networks with time-varying delays,” Neural Networks, vol. 20, no. 8, pp. 868–873, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Z. Yang and D. Xu, “Robust stability of uncertain impulsive control systems with time-varying delay,” Computers & Mathematics with Applications, vol. 53, no. 5, pp. 760–769, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. Yang, T. Huang, L. Zhang, and Z. Yang, “On networked control of impulsive hybrid systems,” Computers & Mathematics with Applications, vol. 61, no. 8, pp. 2076–2080, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. Z. Yang and D. Xu, “Impulsive effects on stability of Cohen-Grossberg neural networks with variable delays,” Applied Mathematics and Computation, vol. 177, no. 1, pp. 63–78, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. C. K. Ahn, “An input-to-state stability approach to filter design for neural networks with noise disturbance,” Advanced Science Letters, vol. 5, pp. 275–278, 2012. View at Publisher · View at Google Scholar
  11. S. Zhu and Y. Shen, “Two algebraic criteria for input-to-state stability of recurrent neural networks with time-varying delays,” Neural Computing and Applications, pp. 1–7, 2012.
  12. C. K. Ahn, “Linear matrix inequality optimization approach to exponential robust filtering for switched Hopfield neural networks,” Journal of Optimization Theory and Applications, vol. 154, no. 2, pp. 573–587, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  13. C. K. Ahn, “An error passivation approach to filtering for switched neural networks with noise disturbance,” Neural Computing and Applications, vol. 21, no. 5, pp. 853–861, 2012. View at Publisher · View at Google Scholar
  14. Z. C. Yang and W. S. Zhou, “Input-to-state stability of impulsive hybrid systems with stochastic effects,” in Proceedings of the 24th IEEE Chinese Control and Decision Conference, pp. 286–291, 2012.
  15. Z. Yang and Y. Hong, “Stabilization of impulsive hybrid systems using quantized input and output feedback,” Asian Journal of Control, vol. 14, no. 3, pp. 679–692, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  16. E. N. Sanchez and J. P. Perez, “Input-to-state stability (ISS) analysis for dynamic neural networks,” IEEE Transactions on Circuits and Systems I, vol. 46, no. 11, pp. 1395–1398, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. C. K. Ahn, “Robust stability of recurrent neural networks with ISS learning algorithm,” Nonlinear Dynamics, vol. 65, no. 4, pp. 413–419, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  18. C. K. Ahn, “2 nonlinear system identification via recurrent neural networks,” Nonlinear Dynamics, vol. 62, no. 3, pp. 543–552, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. C. K. Ahn, “Some new results on stability of Takagi-Sugeno fuzzy Hopfield neural networks,” Fuzzy Sets and Systems, vol. 179, pp. 100–111, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. E. D. Sontag, “Smooth stabilization implies coprime factorization,” IEEE Transactions on Automatic Control, vol. 34, no. 4, pp. 435–443, 1989. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. L. Praly and Z.-P. Jiang, “Stabilization by output feedback for systems with ISS inverse dynamics,” Systems & Control Letters, vol. 21, no. 1, pp. 19–33, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. D. Angeli, E. D. Sontag, and Y. Wang, “A characterization of integral input-to-state stability,” IEEE Transactions on Automatic Control, vol. 45, no. 6, pp. 1082–1097, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. E. D. Sontag and Y. Wang, “On characterizations of the input-to-state stability property,” Systems & Control Letters, vol. 24, no. 5, pp. 351–359, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, vol. 15 of SIAM Studies in Applied Mathematics, SIAM, Philadelphia, Pa, USA, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  25. A. S. Poznyak and E. N. Sanchez, “Nonlinear systems approximation by neural networks: error stability analysis,” Intelligent Automation and Soft Computing, vol. 1, pp. 247–258, 1995.
  26. C. K. Ahn, “A new robust training law for dynamic neural networks with external disturbance: an LMI approach,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 415895, 14 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. J. Hale, Theory of Functional Differential Equations, Springer, New York, NY, USA, 1976.