Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2012, Article ID 426350, 20 pages
http://dx.doi.org/10.1155/2012/426350
Research Article

Combined Convex Technique on Delay-Distribution-Dependent Stability for Delayed Neural Networks

Key Laboratory of Measurement and Control of CSE, School of Automation, Southeast University, Ministry of Education, Nanjing 210096, China

Received 26 March 2012; Revised 27 May 2012; Accepted 27 May 2012

Academic Editor: Zhengqiu Zhang

Copyright © 2012 Ting Wang 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. Zhao, L. Zhang, S. Shen, and H. Gao, “Robust stability criterion for discrete-time uncertain markovian jumping neural networks with defective statistics of modes transitions,” IEEE Transactions on Neural Networks, vol. 22, no. 1, pp. 164–170, 2011. View at Publisher · View at Google Scholar · View at Scopus
  2. Z. Zuo, C. Yang, and Y. Wang, “A new method for stability analysis of recurrent neural networks with interval time-varying delay,” IEEE Transactions on Neural Networks, vol. 21, no. 2, pp. 339–344, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. R. Rakkiyappan, P. Balasubramaniam, and J. Cao, “Global exponential stability results for neutral-type impulsive neural networks,” Nonlinear Analysis, vol. 11, no. 1, pp. 122–130, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. M. Syed Ali and P. Balasubramaniam, “Stability analysis of uncertain fuzzy Hopfield neural networks with time delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 6, pp. 2776–2783, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. J. Tian, D. Xu, and J. Zu, “Novel delay-dependent asymptotic stability criteria for neural networks with time-varying delays,” Journal of Computational and Applied Mathematics, vol. 228, no. 1, pp. 133–138, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. N. Ozcan and S. Arik, “A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays,” Nonlinear Analysis, vol. 10, no. 5, pp. 3312–3320, 2009. View at Publisher · View at Google Scholar
  7. P. Balasubramaniam, V. Vembarasan, and R. Rakkiyappan, “Delay-dependent robust exponential state estimation of Markovian jumping fuzzy Hopfield neural networks with mixed random time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 4, pp. 2109–2129, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. P. Balasubramaniam, R. Krishnasamy, and R. Rakkiyappan, “Delay-dependent stability of neutral systems with time-varying delays using delay-decomposition approach,” Applied Mathematical Modelling, vol. 36, no. 5, pp. 2253–2261, 2012. View at Google Scholar
  9. P. Balasubramaniam, V. Vembarasan, and R. Rakkiyappan, “Leakage delays in T-S fuzzy cellular neural networks,” Neural Processing Letters, vol. 33, no. 2, pp. 111–136, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. H. Li, “Synchronization stability for discrete-time stochastic complex networks with probabilistic interval time-varying delays,” International Journal of Innovative Computing, Information and Control, vol. 7, no. 2, pp. 697–708, 2011. View at Google Scholar · View at Scopus
  11. H. Li, “Cluster synchronization stability for stochastic complex dynamical networks with probabilistic interval time-varying delays,” Journal of Physics A, vol. 44, no. 10, p. 105101, 24, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. H. Li, W. K. Wong, and Y. Tang, “Global synchronization stability for stochastic complex dynamical networks with probabilistic interval time-varying delays,” Journal of Optimization Theory and Applications, vol. 152, no. 2, pp. 496–516, 2012. View at Publisher · View at Google Scholar
  13. Z. Zhang, W. Liu, and D. Zhou, “Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays,” Neural Networks, vol. 25, pp. 94–105, 2012. View at Publisher · View at Google Scholar · View at Scopus
  14. Z. Zhang and D. Zhou, “Global robust exponential stability for second-order Cohen-Grossberg neural networks with multiple delays,” Neurocomputing, vol. 73, no. 1–3, pp. 213–218, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. Z. Zhang, Y. Yang, and Y. Huang, “Global exponential stability of interval general BAM neural networks with reaction-diffusion terms and multiple time-varying delays,” Neural Networks, vol. 24, no. 5, pp. 457–465, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. Z. Zhang, K. Liu, and Y. Yang, “New LMI-based condition on global asymptotic stability concerning BAM neural networks of neutral type,” Neurocomputing, vol. 81, pp. 24–32, 2012. View at Publisher · View at Google Scholar · View at Scopus
  17. X. Li and X. Fu, “Global asymptotic stability of stochastic Cohen-Grossberg-type BAM neural networks with mixed delays: an LMI approach,” Journal of Computational and Applied Mathematics, vol. 235, no. 12, pp. 3385–3394, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. X. Li, “Global robust stability for stochastic interval neural networks with continuously distributed delays of neutral type,” Applied Mathematics and Computation, vol. 215, no. 12, pp. 4370–4384, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  19. X. Li and R. Rakkiyappan, “Delay-dependent global asymptotic stability criteria for stochastic genetic regulatory networks with Markovian jumping parameters,” Applied Mathematical Modelling, vol. 36, no. 4, pp. 1718–1730, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. X. Li, X. Fu, P. Balasubramaniam, and R. Rakkiyappan, “Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations,” Nonlinear Analysis, vol. 11, no. 5, pp. 4092–4108, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. Y. Zhang, D. Yue, and E. Tian, “New stability criteria of neural networks with interval time-varying delay: a piecewise delay method,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 249–259, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  22. S. Mou, H. Gao, J. Lam, and W. Qiang, “A new criterion of delay-dependent asymptotic stability for Hopfield neural networks with time delay,” IEEE Transactions on Neural Networks, vol. 19, no. 3, pp. 532–535, 2008. View at Publisher · View at Google Scholar · View at Scopus
  23. R. Yang, H. Gao, and P. Shi, “Novel robust stability criteria for stochastic Hopfield neural networks with time delays,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 39, no. 2, pp. 467–474, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Zhang, Z. Liu, G. B. Huang, and Z. Wang, “Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay,” IEEE Transactions on Neural Networks, vol. 21, no. 1, pp. 91–106, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. W. H. Chen and W. X. Zheng, “Improved delay-dependent asymptotic stability criteria for delayed neural networks,” IEEE Transactions on Neural Networks, vol. 19, no. 12, pp. 2154–2161, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. X. M. Zhang and Q. L. Han, “New Lyapunov-Krasovskii functionals for global asymptotic stability of delayed neural networks,” IEEE Transactions on Neural Networks, vol. 20, no. 3, pp. 533–539, 2009. View at Publisher · View at Google Scholar · View at Scopus
  27. L. Hu, H. Gao, and W. X. Zheng, “Novel stability of cellular neural networks with interval time-varying delay,” Neural Networks, vol. 21, no. 10, pp. 1458–1463, 2008. View at Publisher · View at Google Scholar · View at Scopus
  28. G. B. Zhang, T. Wang, T. Li, and S. M. Fei, “Delay-derivative-dependent stability criterion for neural networks with proba- bilistic time-varying delay,” International Journal of Systems Science. In press.
  29. Y. Zhang, D. Yue, and E. Tian, “Robust delay-distribution-dependent stability of discrete-time stochastic neural networks with time-varying delay,” Neurocomputing, vol. 72, no. 4–6, pp. 1265–1273, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. D. Yue, Y. Zhang, E. Tian, and C. Peng, “Delay-distribution-dependent exponential stability criteria for discrete-time recurrent neural networks with stochastic delay,” IEEE Transactions on Neural Networks, vol. 19, no. 7, pp. 1299–1306, 2008. View at Publisher · View at Google Scholar · View at Scopus
  31. Y. Tang, J. A. Fang, M. Xia, and D. Yu, “Delay-distribution-dependent stability of stochastic discrete-time neural networks with randomly mixed time-varying delays,” Neurocomputing, vol. 72, no. 16–18, pp. 3830–3838, 2009. View at Publisher · View at Google Scholar · View at Scopus
  32. Y. Zhao, H. Gao, J. Lam, and K. Chen, “Stability analysis of discrete-time recurrent neural networks with stochastic delay,” IEEE Transactions on Neural Networks, vol. 20, no. 8, pp. 1330–1339, 2009. View at Publisher · View at Google Scholar · View at Scopus
  33. J. Fu, H. Zhang, and T. Ma, “Delay-probability-distribution-dependent robust stability analysis for stochastic neural networks with time-varying delay,” Progress in Natural Science, vol. 19, no. 10, pp. 1333–1340, 2009. View at Publisher · View at Google Scholar
  34. M. S. Mahmoud, S. Z. Selim, and P. Shi, “Global exponential stability criteria for neural networks with probabilistic delays,” IET Control Theory & Applications, vol. 4, no. 11, pp. 2405–2415, 2010. View at Publisher · View at Google Scholar
  35. H. Bao and J. Cao, “Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay,” Neural Networks, vol. 24, no. 1, pp. 19–28, 2011. View at Publisher · View at Google Scholar · View at Scopus
  36. C. Peng, D. Yue, E. Tian, and Z. Gu, “A delay distribution based stability analysis and synthesis approach for networked control systems,” Journal of the Franklin Institute. Engineering and Applied Mathematics, vol. 346, no. 4, pp. 349–365, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  37. D. Yue, E. Tian, Z. Wang, and J. Lam, “Stabilization of systems with probabilistic interval input delays and its applications to networked control systems,” IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans, vol. 39, no. 4, pp. 939–945, 2009. View at Publisher · View at Google Scholar · View at Scopus
  38. D. Yue, E. Tian, Y. Zhang, and C. Peng, “Delay-distribution-dependent robust stability of uncertain systems with time-varying delay,” International Journal of Robust and Nonlinear Control, vol. 19, no. 4, pp. 377–393, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  39. D. Yue, E. Tian, Y. Zhang, and C. Peng, “Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay,” IEEE Transactions on Systems, Man, and Cybernetics B, vol. 39, no. 2, pp. 503–516, 2009. View at Publisher · View at Google Scholar · View at Scopus
  40. E. Fridman, U. Shaked, and K. Liu, “New conditions for delay-derivative-dependent stability,” Automatica, vol. 45, no. 11, pp. 2723–2727, 2009. View at Publisher · View at Google Scholar · View at Scopus
  41. P. Park, J. W. Ko, and C. Jeong, “Reciprocally convex approach to stability of systems with time-varying delays,” Automatica, vol. 47, no. 1, pp. 235–238, 2011. View at Publisher · View at Google Scholar · View at Scopus
  42. S. Cong and Y. Zou, “A new delay-dependent exponential stability criterion for Itô stochastic systems with Markovian switching and time-varying delay,” International Journal of Systems Science. Principles and Applications of Systems and Integration, vol. 41, no. 12, pp. 1493–1500, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH