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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 732406, 6 pages
LMI-Based Stability Criteria for Discrete-Time Neural Networks with Multiple Delays
1School of Mathematics, Anhui University, Hefei 230039, China
2Department of Public Teaching, Anhui Business Vocational College, Hefei 230041, China
Received 17 March 2013; Accepted 26 May 2013
Academic Editor: Wen Xiu Ma
Copyright © 2013 Hui Xu and Ranchao Wu. 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.
- S. Mohamad and K. Gopalsamy, “Dynamics of a class of discrete-time neural networks and their continuous-time counterparts,” Mathematics and Computers in Simulation, vol. 53, no. 1-2, pp. 1–39, 2000.
- S. Arik, “An improved global stability result for delayed cellular neural network,” IEEE Transactions on Circuits and Systems, vol. 49, no. 8, pp. 1211–1214, 2002.
- Z. Wang, Y. Liu, and X. Liu, “On global asymptotic stability of neural networks with discrete and distributed delays,” Physics Letters, vol. 345, no. 4–6, pp. 299–308, 2005.
- C.-Y. Cheng, K.-H. Lin, and C.-W. Shih, “Multistability and convergence in delayed neural networks,” Physica D, vol. 225, no. 1, pp. 61–74, 2007.
- 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.
- S. I. Niculescu, Delay Effects on Stability: A Robust Approach, Springer, Berlin, Germany, 2001.
- J. Liang, J. Cao, and J. Lam, “Convergence of discrete-time recurrent neural networks with variable delay,” International Journal of Bifurcation and Chaos, vol. 15, no. 2, pp. 581–595, 2005.
- J. Liang, J. Cao, and D. W. C. Ho, “Discrete-time bidirectional associative memory neural networks with variable delays,” Physics Letters Section A, vol. 335, no. 2-3, pp. 226–234, 2005.
- S. Mohamad, “Global exponential stability in continuous-time and discrete-time delayed bidirectional neural networks,” Physica D, vol. 159, no. 3-4, pp. 233–251, 2001.
- C. Sun and C.-B. Feng, “Discrete-time analogues of integrodifferential equations modeling neural networks,” Physics Letters A, vol. 334, no. 2-3, pp. 180–191, 2005.
- X.-G. Liu, M.-L. Tang, R. Martin, and X.-B. Liu, “Discrete-time BAM neural networks with variable delays,” Physics Letters A, vol. 367, no. 4-5, pp. 322–330, 2007.
- H. Zhao, L. S. Li Sun, and G. Wang, “Periodic oscillation of discrete-time bidirectional associative memory neural networks,” Neurocomputing, vol. 70, no. 16–18, pp. 2924–2930, 2007.
- W. He and J. Cao, “Stability and bifurcation of a class of discrete-time neural networks,” Applied Mathematical Modelling, vol. 31, no. 10, pp. 2111–2122, 2007.
- B. Cessac, “A discrete time neural network model with spiking neurons,” Journal of Mathematical Biology, vol. 56, no. 3, pp. 311–345, 2008.
- Y. Liu, Z. Wang, and X. Liu, “Asymptotic stability for neural networks with mixed time-delays: the discrete-time case,” Neural Networks, vol. 22, no. 1, pp. 67–74, 2009.
- J. Cao and Q. Song, “Global dissipativity on uncertain discrete-time neural networks with time-varying delays,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 810408, 19 pages, 2010.
- 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.
- A. Y. Alanis, E. N. Sanchez, A. G. Loukianov, and E. A. Hernandez, “Discrete-time recurrent high order neural networks for nonlinear identification,” Journal of the Franklin Institute, vol. 347, no. 7, pp. 1253–1265, 2010.
- Z. Huang, X. Wang, and C. Feng, “Multiperiodicity of periodically oscillated discrete-time neural networks with transient excitatory self-connections and sigmoidal nonlinearities,” IEEE Transactions on Neural Networks, vol. 21, no. 10, pp. 1643–1655, 2010.
- C. Li, S. Wu, G. G. Feng, and X. Liao, “Stabilizing effects of impulses in discrete-time delayed neural networks,” IEEE Transactions on Neural Networks, vol. 22, no. 2, pp. 323–329, 2011.
- O. Faydasicok and S. Arik, “Robust stability analysis of a class of neural networks with discrete time delays,” Neural Networks, vol. 29-30, pp. 52–59, 2012.
- Y. 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 Systems, vol. 217, pp. 62–79, 2013.