About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 870486, 8 pages
http://dx.doi.org/10.1155/2013/870486
Research Article

An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays

1College of Mathematics and Computing Science, Changsha University of Science and Technology, Changsha, Hunan 410114, China
2School of Business, Central South University, Changsha, Hunan 410083, China

Received 3 January 2013; Revised 1 March 2013; Accepted 1 March 2013

Academic Editor: Jinde Cao

Copyright © 2013 Chuangxia Huang 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. 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 Zentralblatt MATH · View at MathSciNet
  2. L. O. Chua and L. Yang, “Cellular neural networks: applications,” IEEE Transactions on Circuits and Systems, vol. 35, no. 10, pp. 1273–1290, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  3. T. Chen, “Global exponential stability of delayed Hopfield neural networks,” Neural Networks, vol. 14, no. 8, pp. 977–980, 2001. View at Publisher · View at Google Scholar · View at Scopus
  4. K. Lu, D. Xu, and Z. Yang, “Global attraction and stability for Cohen-Grossberg neural networks with delays,” Neural Networks, vol. 19, no. 10, pp. 1538–1549, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  5. J. Cao and L. Li, “Cluster synchronization in an array of hybrid coupled neural networks with delay,” Neural Networks, vol. 22, no. 4, pp. 335–342, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. T. Roska, T. Boros, P. Thiran, and L. Chua, “Detecting simple motion using cellular neural networks,” in Proceedings of the International Workshop Cellular neural networks Application, pp. 127–138, 1990.
  7. T. Roska and L. O. Chua, “Cellular neural networks with non-linear and delay-type template elements and non-uniform grids,” International Journal of Circuit Theory and Applications, vol. 20, no. 5, pp. 469–481, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. J. Cao, “A set of stability criteria for delayed cellular neural networks,” IEEE Transactions on Circuits and Systems. I., vol. 48, no. 4, pp. 494–498, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. J. Cao, G. Feng, and Y. Wang, “Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions,” Physica D, vol. 237, no. 13, pp. 1734–1749, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Jiang and Z. Teng, “Global eponential stability of cellular neural networks with time-varying coefficients and delays,” Neural Networks, vol. 17, no. 10, pp. 1415–1425, 2004. View at Publisher · View at Google Scholar · View at Scopus
  11. J. Zhao, D. J. Hill, and T. Liu, “Synchronization of complex dynamical networks with switching topology: a switched system point of view,” Automatica, vol. 45, no. 11, pp. 2502–2511, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Lu, D. W. C. Ho, and L. Wu, “Exponential stabilization of switched stochastic dynamical networks,” Nonlinearity, vol. 22, no. 4, pp. 889–911, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. H. Huang, Y. Qu, and H. X. Li, “Robust stability analysis of switched Hopfield neural networks with time-varying delay under uncertainty,” Physics Letters A, vol. 345, no. 4–6, pp. 345–354, 2005. View at Publisher · View at Google Scholar · View at Scopus
  14. D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, no. 5, pp. 59–70, 1999. View at Publisher · View at Google Scholar · View at Scopus
  15. W. Yu, J. Cao, and W. Lu, “Synchronization control of switched linearly coupled neural networks with delay,” Neurocomputing, vol. 73, no. 4–6, pp. 858–866, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. W.-A. Zhang and L. Yu, “Stability analysis for discrete-time switched time-delay systems,” Automatica, vol. 45, no. 10, pp. 2265–2271, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. H. Huang, Y. Qu, and H. Li, “Robust stability analysis of switched hop?eld neural networks with time-varying delay under uncertainty,” Physics Letters A, vol. 345, pp. 345–354, 2005. View at Publisher · View at Google Scholar
  18. P. Li and J. Cao, “Global stability in switched recurrent neural networks with time-varying delay via nonlinear measure,” Nonlinear Dynamics, vol. 49, no. 1-2, pp. 295–305, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. 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
  20. J. Lian and K. Zhang, “Exponential stability for switched Cohen-Grossberg neural networks with average dwell time,” Nonlinear Dynamics, vol. 63, no. 3, pp. 331–343, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  21. D. Xie, Q. Wang, and Y. Wu, “Average dwell-time approach to L2 gain control synthesis of switched linear systems with time delay in detection of switching signal,” IET Control Theory & Applications, vol. 3, no. 6, pp. 763–771, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  22. X.-M. Sun, J. Zhao, and D. J. Hill, “Stability and L2-gain analysis for switched delay systems: a delay-dependent method,” Automatica, vol. 42, no. 10, pp. 1769–1774, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  23. C. Huang and J. Cao, “Convergence dynamics of stochastic Cohen-Grossberg neural networks with unbounded distributed delays,” IEEE Transactions on Neural Networks, vol. 22, no. 4, pp. 561–572, 2011. View at Publisher · View at Google Scholar · View at Scopus
  24. J. Cao and J. Liang, “Boundedness and stability for Cohen-Grossberg neural network with time-varying delays,” Journal of Mathematical Analysis and Applications, vol. 296, no. 2, pp. 665–685, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. H. Zhang, Z. Yi, and L. Zhang, “Continuous attractors of a class of recurrent neural networks,” Computers & Mathematics with Applications, vol. 56, no. 12, pp. 3130–3137, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. J. P. Hespanha and A. S. Morse, “Stability of switched systems with average dwell-time,” in Proceedings of the 38th IEEE Conference on Decision and Control (CDC '99), pp. 2655–2660, December 1999. View at Scopus