Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2014, Article ID 263847, 9 pages
http://dx.doi.org/10.1155/2014/263847
Research Article

Global -Stability of Complex-Valued Neural Networks with Unbounded Time-Varying Delays

1Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China
2School of Computer Science and Technology, Nanjing University of Science and Technology, Nanjing 210094, China
3Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

Received 4 January 2014; Revised 23 February 2014; Accepted 25 February 2014; Published 3 April 2014

Academic Editor: Derui Ding

Copyright © 2014 Xiaofeng Chen 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. H. Dong, Z. Wang, and H. Gao, “Distributed H filtering for a class of Markovian jump nonlinear time-delay systems over lossy sensor networks,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4665–4672, 2013. View at Google Scholar
  2. J. Hu, Z. Wang, B. Shen, and H. Gao, “Quantised recursive filtering for a class of nonlinear systems with multiplicative noises and missing measurements,” International Journal of Control, vol. 86, no. 4, pp. 650–663, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. Y. Fang, K. Yan, and K. Li, “Impulsive synchronization of a class of chaotic systems,” Systems Science and Control Engineering, vol. 2, no. 1, pp. 55–60, 2014. View at Google Scholar
  4. M. Darouach and M. Chadli, “Admissibility and control of switched discrete-time singular systems,” Systems Science and Control Engineering, vol. 1, no. 1, pp. 43–51, 2013. View at Google Scholar
  5. B. Shen, Z. Wang, D. Ding, and H. Shu, “H state estimation for complex networks with uncertain inner coupling and incomplete measurements,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 12, pp. 2027–2037, 2013. View at Google Scholar
  6. B. Shen, Z. Wang, and X. Liu, “Sampled-data synchronization control of dynamical networks with stochastic sampling,” IEEE Transactions on Automatic Control, vol. 57, no. 10, pp. 2644–2650, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  7. J. Liang, Z. Wang, Y. Liu, and X. Liu, “State estimation for two-dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays,” International Journal of Robust and Nonlinear Control, vol. 24, no. 1, pp. 18–38, 2014. View at Google Scholar
  8. X. Kan, Z. Wang, and H. Shu, “State estimation for discrete-time delayed neural networks with fractional uncertainties and sensor saturations,” Neurocomputing, vol. 117, pp. 64–71, 2013. View at Google Scholar
  9. Z. Wang, B. Zineddin, J. Liang et al., “A novel neural network approach to cDNA microarray image segmentation,” Computer Methods and Programs in Biomedicine, vol. 111, no. 1, pp. 189–198, 2013. View at Google Scholar
  10. A. Hirose, Complex-Valued Neural Networks, Springer; Heidelberg GmbH and Co. K, Berlin, Germany, 2012.
  11. G. Tanaka and K. Aihara, “Complex-valued multistate associative memory with nonlinear multilevel functions for gray-level image reconstruction,” IEEE Transactions on Neural Networks, vol. 20, no. 9, pp. 1463–1473, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Chen, L. Hanzo, and S. Tan, “Symmetric complex-valued RBF receiver for multiple-antenna-aided wireless systems,” IEEE transactions on Neural Networks, vol. 19, no. 9, pp. 1659–1665, 2008. View at Google Scholar · View at Scopus
  13. I. Cha and S. A. Kassam, “Channel equalization using adaptive complex radial basis function networks,” IEEE Journal on Selected Areas in Communications, vol. 13, no. 1, pp. 122–131, 1995. View at Publisher · View at Google Scholar · View at Scopus
  14. T. Nitta, “Orthogonality of decision boundaries in complex-valued neural networks,” Neural Computation, vol. 16, no. 1, pp. 73–97, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Faijul Amin and K. Murase, “Single-layered complex-valued neural network for real-valued classification problems,” Neurocomputing, vol. 72, no. 4–6, pp. 945–955, 2009. View at Publisher · View at Google Scholar · View at Scopus
  16. B. K. Tripathi and P. K. Kalra, “On efficient learning machine with root-power mean neuron in complex domain,” IEEE Transactions on Neural Networks, vol. 22, no. 5, pp. 727–738, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. J. H. Mathews and R. W. Howell, Complex Analysis for Mathematics and Engineering, Jones and Bartlett Publications, 3rd edition, 1997.
  18. J. Hu and J. Wang, “Global stability of complex-valued recurrent neural networks with time-delays,” IEEE Transactions on Neural Networks, vol. 23, no. 6, pp. 853–865, 2012. View at Google Scholar
  19. V. S. H. Rao and G. R. Murthy, “Global dynamics of a class of complex valued neural networks,” International Journal of Neural Systems, vol. 18, no. 2, pp. 165–171, 2008. View at Publisher · View at Google Scholar · View at Scopus
  20. W. Zhou and J. M. Zurada, “Discrete-time recurrent neural networks with complex-valued linear threshold neurons,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 56, no. 8, pp. 669–673, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. C. Duan and Q. Song, “Boundedness and stability for discrete-time delayed neural network with complex-valued linear threshold neurons,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 368379, 19 pages, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. B. Zou and Q. Song, “Boundedness and complete stability of complex-valued neural networks with time delay,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 8, pp. 1227–1238, 2013. View at Google Scholar
  23. X. Xu, J. Zhang, and J. Shi, “Exponential stability of complex-valued neural networks with mixed delays,” Neurocomputing, vol. 128, pp. 483–490, 2014. View at Google Scholar
  24. X. Chen and Q. Song, “Global stability of complex-valued neural networks with both leakage time delay and discrete time delay on time scales,” Neurocomputing, vol. 121, pp. 254–264, 2013. View at Google Scholar
  25. S.-I. Niculescu, Delay Effects on Stability: A Robust Control Approach, Springer, London, UK, 2001. View at MathSciNet
  26. V. B. Kolmanovskiĭ and V. R. Nosov, Stability of Functional-Differential Equations, Academic Press, London, UK, 1986. View at MathSciNet
  27. Y. Liu, Z. Wang, J. Liang, and X. Liu, “Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays,” IEEE Transactions on Cybernetics, vol. 43, no. 1, pp. 102–114, 2013. View at Google Scholar
  28. T. Chen and L. Wang, “Power-rate global stability of dynamical systems with unbounded time-varying delays,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 54, no. 8, pp. 705–709, 2007. View at Publisher · View at Google Scholar · View at Scopus
  29. T. Chen and L. Wang, “Global μ-stability of delayed neural networks with unbounded time-varying delays,” IEEE Transactions on Neural Networks, vol. 18, no. 6, pp. 1836–1840, 2007. View at Publisher · View at Google Scholar · View at Scopus
  30. X. Liu and T. Chen, “Robust μ-stability for uncertain stochastic neural networks with unbounded time-varying delays,” Physica A: Statistical Mechanics and Its Applications, vol. 387, no. 12, pp. 2952–2962, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  31. X. Liu and J. Cao, “On periodic solutions of neural networks via differential inclusions,” Neural Networks, vol. 22, no. 4, pp. 329–334, 2009. View at Publisher · View at Google Scholar · View at Scopus
  32. X. Liu and J. Cao, “Robust state estimation for neural networks with discontinuous activations,” IEEE Transactions on Systems, Man, and Cybernetics B: Cybernetics, vol. 40, no. 6, pp. 1425–1437, 2010. View at Google Scholar · View at Scopus
  33. X. Liu, T. Chen, J. Cao, and W. Lu, “Dissipativity and quasi-synchronization for neural networks with discontinuous activations and parameter mismatches,” Neural Networks, vol. 24, no. 10, pp. 1013–1021, 2011. View at Publisher · View at Google Scholar · View at Scopus
  34. X. Liu, J. Cao, and W. Yu, “Filippov systems and quasi-synchronization control for switched networks,” Chaos, vol. 22, no. 3, Article ID 033110, 2012. View at Google Scholar