About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 647231, 18 pages
http://dx.doi.org/10.1155/2012/647231
Research Article

Global Robust Exponential Stability Analysis for Interval Neural Networks with Mixed Delays

Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China

Received 17 September 2012; Revised 21 November 2012; Accepted 21 November 2012

Academic Editor: Józef Banaś

Copyright © 2012 Yanke Du and Rui Xu. 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. S. Arik, “Global robust stability analysis of neural networks with discrete time delays,” Chaos, Solitons and Fractals, vol. 26, no. 5, pp. 1407–1414, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. T. Ensari and S. Arik, “New results for robust stability of dynamical neural networks with discrete time delays,” Expert Systems with Applications, vol. 37, no. 8, pp. 5925–5930, 2010. View at Publisher · View at Google Scholar · View at Scopus
  3. O. Faydasicok and S. Arik, “Further analysis of global robust stability of neural networks with multiple time delays,” Journal of the Franklin Institute, vol. 349, no. 3, pp. 813–825, 2012. View at Publisher · View at Google Scholar
  4. O. Faydasicok and S. Arik, “A new robust stability criterion for dynamical neural networks with multiple time delays,” Neurocomputing, vol. 99, no. 1, pp. 290–297, 2013.
  5. W. Han, Y. Liu, and L. Wang, “Robust exponential stability of Markovian jumping neural networks with mode-dependent delay,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2529–2535, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. N. Ozcan and S. Arik, “Global robust stability analysis of neural networks with multiple time delays,” IEEE Transactions on Circuits and Systems I, vol. 53, no. 1, pp. 166–176, 2006. View at Publisher · View at Google Scholar
  7. V. Singh, “Improved global robust stability criterion for delayed neural networks,” Chaos, Solitons and Fractals, vol. 31, no. 1, pp. 224–229, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. W. Zhao and Q. Zhu, “New results of global robust exponential stability of neural networks with delays,” Nonlinear Analysis: Real World Applications, vol. 11, no. 2, pp. 1190–1197, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. F. Wang and H. Wu, “Mean square exponential stability and periodic solutions of stochastic interval neural networks with mixed time delays,” Neurocomputing, vol. 73, no. 16–18, pp. 3256–3263, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. P. Balasubramaniam and G. Nagamani, “A delay decomposition approach to delay-dependent passivity analysis for interval neural networks with time-varying delay,” Neurocomputing, vol. 74, no. 10, pp. 1646–1653, 2011. View at Publisher · View at Google Scholar · View at Scopus
  11. P. Balasubramaniam, G. Nagamani, and R. Rakkiyappan, “Global passivity analysis of interval neural networks with discrete and distributed delays of neutral type,” Neural Processing Letters, vol. 32, no. 2, pp. 109–130, 2010. View at Publisher · View at Google Scholar · View at Scopus
  12. P. Balasubramaniam and M. S. Ali, “Robust exponential stability of uncertain fuzzy Cohen-Grossberg neural networks with time-varying delays,” Fuzzy Sets and Systems, vol. 161, no. 4, pp. 608–618, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. O. M. Kwon, S. M. Lee, and J. H. Park, “Improved delay-dependent exponential stability for uncertain stochastic neural networks with time-varying delays,” Physics Letters A, vol. 374, no. 10, pp. 1232–1241, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Lakshmanan, A. Manivannan, and P. Balasubramaniam, “Delay-distribution-dependent stability criteria for neural networks with time-varying delays,” Dynamics of Continuous, Discrete and Impulsive Systems A, vol. 19, no. 1, pp. 1–14, 2012.
  15. J. L. Shao, T. Z. Huang, and X. P. Wang, “Improved global robust exponential stability criteria for interval neural networks with time-varying delays,” Expert Systems with Applications, vol. 38, no. 12, pp. 15587–15593, 2011. View at Publisher · View at Google Scholar · View at Scopus
  16. J. L. Shao, T. Z. Huang, and S. Zhou, “An analysis on global robust exponential stability of neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 7–9, pp. 1993–1998, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. J.-L. Shao, T.-Z. Huang, and S. Zhou, “Some improved criteria for global robust exponential stability of neural networks with time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 3782–3794, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  18. Z. Wang, H. Zhang, and W. Yu, “Robust stability criteria for interval Cohen-Grossberg neural networks with time varying delay,” Neurocomputing, vol. 72, no. 4–6, pp. 1105–1110, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. H. Zhang, Z. Wang, and D. Liu, “Robust exponential stability of recurrent neural networks with multiple time-varying delays,” IEEE Transactions on Circuits and Systems II, vol. 54, no. 8, pp. 730–734, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Zhang, “Global exponential stability of interval neural networks with variable delays,” Applied Mathematics Letters, vol. 19, no. 11, pp. 1222–1227, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  21. 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
  22. W. Su and Y. Chen, “Global robust stability criteria of stochastic Cohen-Grossberg neural networks with discrete and distributed time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 2, pp. 520–528, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  23. H. Liu, Y. Ou, J. Hu, and T. Liu, “Delay-dependent stability analysis for continuous-time BAM neural networks with Markovian jumping parameters,” Neural Networks, vol. 23, no. 3, pp. 315–321, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Pan, X. Liu, and S. Zhong, “Stability criteria for impulsive reaction-diffusion Cohen-Grossberg neural networks with time-varying delays,” Mathematical and Computer Modelling, vol. 51, no. 9-10, pp. 1037–1050, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  25. J. Tian and S. Zhong, “Improved delay-dependent stability criterion for neural networks with time-varying delay,” Applied Mathematics and Computation, vol. 217, no. 24, pp. 10278–10288, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  26. H. Wang, Q. Song, and C. Duan, “LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions,” Mathematics and Computers in Simulation, vol. 81, no. 4, pp. 837–850, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  27. X. Zhang, S. Wu, and K. Li, “Delay-dependent exponential stability for impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1524–1532, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  28. K. Li, “Stability analysis for impulsive Cohen-Grossberg neural networks with time-varying delays and distributed delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 2784–2798, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  29. X. Fu and X. Li, “LMI conditions for stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 435–454, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  30. B. Zhou, Q. Song, and H. Wang, “Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales,” Neurocomputing, vol. 74, no. 17, pp. 3142–3150, 2011. View at Publisher · View at Google Scholar · View at Scopus
  31. R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, UK, 1991. View at Publisher · View at Google Scholar
  32. J. C. Principe, J. M. Kuo, and S. Celebi, “An analysis of the gamma memory in dynamic neural networks,” IEEE Transactions on Neural Networks, vol. 5, no. 2, pp. 331–337, 1994. View at Publisher · View at Google Scholar · View at Scopus