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Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 325371, 14 pages
http://dx.doi.org/10.1155/2011/325371
Research Article

Delay-Dependent Stability Criteria of Uncertain Periodic Switched Recurrent Neural Networks with Time-Varying Delays

1College of Computer Science, Panzhihua University, Panzhihua 617000, China
2School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 219004, China

Received 20 June 2011; Revised 29 August 2011; Accepted 17 September 2011

Academic Editor: Baodong Zheng

Copyright © 2011 Xing Yin et al. 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. Y. Liu, Z. Wang, A. Serrano, and X. Liu, “Discrete-time recurrent neural networks with time-varying delays: exponential stability analysis,” Physics Letters Section A, vol. 362, no. 5-6, pp. 480–488, 2007. View at Publisher · View at Google Scholar · View at Scopus
  2. Q. Song and Z. Wang, “A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays,” Physics Letters Section A, vol. 368, no. 1-2, pp. 134–145, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. B. Zhang, S. Xu, and Y. Zou, “Improved delay-dependent exponential stability criteria for discrete-time recurrent neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 1–3, pp. 321–330, 2008. View at Publisher · View at Google Scholar · View at Scopus
  4. H. Huang, G. Feng, and J. Cao, “Robust state estimation for uncertain neural networks with time-varying delay,” IEEE Transactions on Neural Networks, vol. 19, no. 8, pp. 1329–1339, 2008. View at Publisher · View at Google Scholar · View at Scopus
  5. Y. Shen and J. Wang, “An improved algebraic criterion for global exponential stability of recurrent neural networks with time-varying delays,” IEEE Transactions on Neural Networks, vol. 19, no. 3, pp. 528–531, 2008. View at Publisher · View at Google Scholar · View at Scopus
  6. Q. Song and J. Cao, “Global dissipativity on uncertain discrete-time neural networks with time-varying delays,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 810408, 19 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. Y. Liu, Z. Wang, and X. Liu, “Asymptotic stability for neural networks with mixed time-delays: the discrete-time case,” Neural Networks, vol. 22, no. 1, pp. 67–74, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Wu, F. Liu, P. Shi, Y. He, and R. Yokoyama, “Improved free-weighting matrix approach for stability analysis of discrete-time recurrent neural networks with time-varying delay,” IEEE Transactions on Circuits and Systems II, vol. 55, no. 7, pp. 690–694, 2008. View at Publisher · View at Google Scholar · View at Scopus
  9. C. Li, S. Wu, G. G. Feng, and X. Liao, “Stabilizing effects of impulses in discrete-time delayed neural networks,” IEEE Transactions on Neural Networks, vol. 22, no. 2, pp. 323–329, 2011. View at Publisher · View at Google Scholar
  10. H. Xiang, K. M. Yan, and B. Y. Wang, “Existence and global exponential stability of periodic solution for delayed high-order Hopfield-type neural networks,” Physics Letters Section A, vol. 352, no. 4-5, pp. 341–349, 2006. View at Publisher · View at Google Scholar · View at Scopus
  11. H. Xiang, K. M. Yan, and B. Y. Wang, “Existence and global stability of periodic solution for delayed discrete high-order Hopfield-type neural networks,” Discrete Dynamics in Nature and Society, vol. 2005, no. 3, pp. 281–297, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. G. Shaikhet and L. Shaikhet, “Stability of stochastic linear difference equations with varying delay,” in Advances in Systems, Signals, Control and Computers, V. Bajic, Ed., pp. 101–104, IAAMSAD and SA branch of the Academy of Nonlinear Sciences, Durban, South Africa, 1998. View at Google Scholar
  13. J. Li, Y. Diao, M. Li, and X. Yin, “Stability analysis of Discrete Hopfield neural networks with the nonnegative definite monotone increasing weight function matrix,” Discrete Dynamics in Nature and Society, vol. 2009, Article ID 673548, 2009. View at Publisher · View at Google Scholar
  14. J. Li, Y. Diao, J. Mao, Y. Zhang, and X. Yin, “Stability analysis of discrete hopfield neural networks with weight function matrix,” Lecture Notes in Computer Science, vol. 5370, pp. 760–768, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. X. Wu, Y. Wang, L. Huang, and Y. Zuo, “Robust exponential stability criterion for uncertain neural networks with discontinuous activation functions and time-varying delays,” Neurocomputing, vol. 73, no. 7–9, pp. 1265–1271, 2010. View at Publisher · View at Google Scholar
  16. H. Wu, W. Feng, and X. Liang, “New stability criteria for uncertain neural networks with interval time-varying delays,” Cognitive Neurodynamics, vol. 2, no. 4, pp. 363–370, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. C. Y. Lu, H. H. Tsai, T. J. Su, J. S. H. Tsai, and C. W. Liao, “A delay-dependent approach to passivity analysis for uncertain neural networks with time-varying Delayd,” Neural Processing Letters, vol. 27, no. 3, pp. 237–246, 2008. View at Publisher · View at Google Scholar · View at Scopus
  18. X. Lou and B. Cui, “Delay-dependent criteria for global robust periodicity of uncertain switched recurrent neural networks with time-varying delay,” IEEE Transactions on Neural Networks, vol. 19, no. 4, pp. 549–557, 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. J. Liang, Z. Wang, Y. Liu, and X. Liu, “Robust synchronization of an array of coupled stochastic discrete-time delayed neural networks,” IEEE Transactions on Neural Networks, vol. 19, no. 11, pp. 1910–1921, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. H. Zhang and Y. Wang, “Stability analysis of Markovian jumping stochastic Cohen-Grossberg neural networks with mixed time delays,” IEEE Transactions on Neural Networks, vol. 19, no. 2, pp. 366–370, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. Z. Wang, Y. Liu, and X. Liu, “State estimation for jumping recurrent neural networks with discrete and distributed delays,” Neural Networks, vol. 22, no. 1, pp. 41–48, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Zhou, Q. Song, and J. Yang, “Stochastic passivity of uncertain neural networks with time-varying delays,” Abstract and Applied Analysis, vol. 2009, Article ID 725846, 16 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. E. Zhu, Y. Wang, Y. Wang, H. Zhang, and J. Zou, “Stability analysis of recurrent neural networks with random delay and markovian switching,” Journal of Inequalities and Applications, vol. 2010, Article ID 191546, 2010. View at Publisher · View at Google Scholar
  24. J. Li, W. Wu, J. Yuan, Q. Tan, and X. Yin, “Delay-dependent stability criterion of arbitrary switched linear systems with time-varying delay,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 347129, 16 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. B. Chen and J. Wang, “Global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time-varying delays,” IEEE Transactions on Neural Networks, vol. 16, no. 6, pp. 1440–1448, 2005. View at Publisher · View at Google Scholar · View at Scopus