Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2014, Article ID 906439, 13 pages
http://dx.doi.org/10.1155/2014/906439
Research Article

State Estimation for Discrete-Time Fuzzy Cellular Neural Networks with Mixed Time Delays

1Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering College, Shijiazhuang 050003, China
2College of Mathematics and Information Technology, Xingtai University, Xingtai 054001, China

Received 26 December 2013; Accepted 10 March 2014; Published 29 April 2014

Academic Editor: Qintao Gan

Copyright © 2014 Lijie Geng 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. L. O. Chua and L. B. Yang, “Cellular neural networks: theory,” IEEE Transactions on Circuits and Systems, vol. 35, no. 10, pp. 1257–1272, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. T. Yang, L.-B. Yang, C. W. Wu, and L. O. Chua, “Fuzzy cellular neural networks: theory,” in Proceedings of the 4th IEEE International Workshop on Cellular Neural Networks, and Their Applications, pp. 181–186, June 1996. View at Scopus
  3. T. Yang, L.-B. Yang, C. W. Wu, and L. O. Chua, “Fuzzy cellular neural networks: applications,” in Proceedings of the 4th IEEE International Workshop on Cellular Neural Networks, and Their Applications, pp. 225–230, June 1996. View at Scopus
  4. M. Syed Ali and P. Balasubramaniam, “Global asymptotic stability of stochastic fuzzy cellular neural networks with multiple discrete and distributed time-varying delays,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 7, pp. 2907–2916, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. K. Yuan, J. Cao, and J. M. Deng, “Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays,” Neurocomputing, vol. 69, no. 13–15, pp. 1619–1627, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. Z. W. Liu, H. G. Zhang, and Z. S. Wang, “Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 4-6, pp. 1056–1064, 2009. View at Publisher · View at Google Scholar · View at Scopus
  7. X. D. Li, R. Rakkiyappan, and P. Balasubramaniam, “Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations,” Journal of the Franklin Institute, vol. 348, no. 2, pp. 135–155, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. X. M. Feng, F. Q. Zhang, and W. J. Wang, “Global exponential synchronization of delayed fuzzy cellular neural networks with impulsive effects,” Chaos, Solitons and Fractals, vol. 44, no. 1–3, pp. 9–16, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  9. Q. T. Gan, R. Xu, and P. H. Yang, “Exponential synchronization of stochastic fuzzy cellular neural networks with time delay in the leakage term and reaction-diffusion,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 4, pp. 1862–1870, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. Y. R. Liu, Z. D. Wang, and X. H. 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
  11. H. W. Wang and Q. K. Song, “Synchronization for an array of coupled stochastic discrete-time neural networks with mixed delays,” Neurocomputing, vol. 74, no. 10, pp. 1572–1584, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. H. Y. Li, C. Wang, P. Shi, and H. J. Gao, “New passivity results for uncertain discrete-time stochastic neural networks with mixed time delays,” Neurocomputing, vol. 73, no. 16-18, pp. 3291–3299, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. T. Li, A. G. Song, and S. M. Fei, “Synchronization control for arrays of coupled discrete-time delayed Cohen-Grossberg neural networks,” Neurocomputing, vol. 74, no. 1–3, pp. 197–204, 2010. View at Publisher · View at Google Scholar · View at Scopus
  14. M. J. Park, O. M. Kwon, S. M. Li, and E. J. Cha, “On synchronization criterion for coupled discrete-time neural networks with interval time-varying delays,” Neurocomputing, vol. 99, no. 1, pp. 188–196, 2013. View at Google Scholar
  15. L. Tian, J. L. Liang, and J. D. Chao, “Robust observer for discrete-time Markovian jumping neural networks with mixed mode-dependent delays,” Nonlinear Dynamics, vol. 67, no. 1, pp. 47–61, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. D. Zhang and L. Yu, “Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays,” Nonlinear Dynamics, vol. 67, no. 1, pp. 403–411, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  17. Z. G. Wu, P. Shi, H. Y. Su, and J. Chu, “Dissipativity analysis for discrete-time stochastic neural networks with time-varying delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 3, pp. 345–355, 2013. View at Google Scholar
  18. Q. K. Song and J. D. Cao, “Dynamical behaviors of discrete-time fuzzy cellular neural networks with variable delays and impulses,” Journal of the Franklin Institute, vol. 345, no. 1, pp. 39–59, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  19. Y. K. Li and C. Wang, “Existence and global exponential stability of equilibrium for discrete-time fuzzy BAM neural networks with variable delays and impulses,” Fuzzy Sets and Systems, vol. 217, pp. 62–79, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  20. Y. R. Liu, Z. D. Wang, and X. H. Liu, “State estimation for discrete-time Markovian jumping neural networks with mixed mode-dependent delays,” Physics Letters A: General, Atomic and Solid State Physics, vol. 372, no. 48, pp. 7147–7155, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  21. H. B. Bao and J. D. 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
  22. S. Lakshmanan, J. H. Park, H. Y. Jung, and P. Balasubramaniam, “Design of state estimator for neural networks with leakage, discrete and distributed delays,” Applied Mathematics and Computation, vol. 218, no. 22, pp. 11297–11310, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Z. Wang, Y. Liu, X. Liu, and Y. Shi, “Robust state estimation for discrete-time stochastic neural networks with probabilistic measurement delays,” Neurocomputing, vol. 74, no. 1–3, pp. 256–264, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. Z. G. Wu, H. Y. Su, and J. Chu, “State estimation for discrete Markovian jumping neural networks with time delay,” Neurocomputing, vol. 73, no. 10–12, pp. 2247–2254, 2010. View at Publisher · View at Google Scholar · View at Scopus
  25. D. Zhang and L. Yu, “Exponential state estimation for Markovian jumping neural networks with time-varying discrete and distributed delays,” Neural Networks, vol. 35, no. 11, pp. 103–111, 2012. View at Google Scholar
  26. D. Zhang, L. Yu, Q. G. Wang, and C. J. Ong, “Estimator design for discrete-time switched neural networks with asynchronous switching and time-varying delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 5, pp. 827–834, 2012. View at Google Scholar
  27. P. Balasubramaniam, M. Kalpana, and R. Rakkiyappan, “State estimation for fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays,” Computers and Mathematics with Applications, vol. 62, no. 10, pp. 3959–3972, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  28. Y. R. Liu, Z. D. Wang, and X. H. Liu, “Global exponential stability of generalized recurrent neural networks with discrete and distributed delays,” Neural Networks, vol. 19, no. 5, pp. 667–675, 2006. View at Publisher · View at Google Scholar · View at Scopus
  29. Y. R. Liu, Z. D. Wang, J. L. Liang, and X. H. Liu, “Synchronization and state estimation for discrete-time complex networks with distributed delays,” IEEE Transactions on Systems, Man, and Cybernetics, B: Cybernetics, vol. 38, no. 5, pp. 1314–1325, 2008. View at Publisher · View at Google Scholar · View at Scopus
  30. J. Sun, G. P. Liu, and J. Chen, “Delay-dependent stability and stabilization of neutral time-delay systems,” International Journal of Robust and Nonlinear Control, vol. 19, no. 10, pp. 1364–1375, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  31. Q. K. Song and Z. D. Wang, “A delay-dependent LMI approach to dynamics analysis of discrete-time recurrent neural networks with time-varying delays,” Physics Letters A: General, Atomic and Solid State Physics, vol. 368, no. 1-2, pp. 134–145, 2007. View at Publisher · View at Google Scholar · View at Scopus
  32. S. S. Mou, H. J. Gao, W. Y. Qiang, and Z. Y. Fei, “State estimation for discrete-time neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 1–3, pp. 643–647, 2008. View at Publisher · View at Google Scholar · View at Scopus