Abstract and Applied Analysis
Volume 2009 (2009), Article ID 725846, 16 pages
doi:10.1155/2009/725846
Research Article
Stochastic Passivity of Uncertain Neural Networks with Time-Varying Delays
1College of Civil Engineering and Architecture, Chongqing Jiaotong University, Chongqing 400074, China
2Department of Mathematics, Chongqing Jiaotong University, Chongqing 400074, China
Received 22 July 2009; Accepted 18 October 2009
Academic Editor: Elena Litsyn
Copyright © 2009 Jianting Zhou 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
- Ju H. Park and O. M. Kwon, “Delay-dependent stability criterion for bidirectional associative memory neural networks with interval time-varying delays,” Modern Physics Letters B, vol. 23, no. 1, pp. 35–46, 2009. View at Publisher · View at Google Scholar · View at Scopus
- K. Gopalsamy, “Stability of artificial neural networks with impulses,” Applied Mathematics and Computation, vol. 154, no. 3, pp. 783–813, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- S. Arik, “An analysis of exponential stability of delayed neural networks with time varying delays,” Neural Networks, vol. 17, no. 7, pp. 1027–1031, 2004. View at Publisher · View at Google Scholar · View at PubMed · View at Zentralblatt MATH · View at Scopus
- W. Lu and T. Chen, “Dynamical behaviors of Cohen-Grossberg neural networks with discontinuous activation functions,” Neural Networks, vol. 18, no. 3, pp. 231–242, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- T. Chen and L. Wang, “Global -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
- J. Cao and X. Li, “Stability in delayed Cohen-Grossberg neural networks: LMI optimization approach,” Physica D, vol. 212, no. 1-2, pp. 54–65, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Ju H. Park and O. M. Kwon, “Further results on state estimation for neural networks of neutral-type with time-varying delay,” Applied Mathematics and Computation, vol. 208, no. 1, pp. 69–75, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Ju H. Park, “Global exponential stability of cellular neural networks with variable delays,” Applied Mathematics and Computation, vol. 183, no. 2, pp. 1214–1219, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Ju H. Park, “On global stability criterion for neural networks with discrete and distributed delays,” Chaos, Solitons & Fractals, vol. 30, no. 4, pp. 897–902, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Y. Liu, Z. Wang, and X. 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 PubMed · View at Zentralblatt MATH · View at Scopus
- N. Ozcan and S. Arik, “A new sufficient condition for global robust stability of bidirectional associative memory neural networks with multiple time delays,” Nonlinear Analysis: Real World Applications, vol. 10, no. 5, pp. 3312–3320, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- V. Singh, “Novel global robust stability criterion for neural networks with delay,” Chaos, Solitons & Fractals, vol. 41, no. 1, pp. 348–353, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
- Ju H. Park, “Further note on global exponential stability of uncertain cellular neural networks with variable delays,” Applied Mathematics and Computation, vol. 188, no. 1, pp. 850–854, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- O. M. Kwon and Ju H. Park, “Exponential stability analysis for uncertain neural networks with interval time-varying delays,” Applied Mathematics and Computation, vol. 212, no. 2, pp. 530–541, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Z. Wang, Y. Liu, K. Fraser, and X. Liu, “Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays,” Physics Letters A, vol. 354, no. 4, pp. 288–297, 2006. View at Publisher · View at Google Scholar · View at Scopus
- X. Wang, Q. Guo, and D. Xu, “Exponential -stability of impulsive stochastic Cohen-Grossberg neural networks with mixed delays,” Mathematics and Computers in Simulation, vol. 79, no. 5, pp. 1698–1710, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- P. Balasubramaniam and R. Rakkiyappan, “Global asymptotic stability of stochastic recurrent neural networks with multiple discrete delays and unbounded distributed delays,” Applied Mathematics and Computation, vol. 204, no. 2, pp. 680–686, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- C. Huang, Y. He, and H. Wang, “Mean square exponential stability of stochastic recurrent neural networks with time-varying delays,” Computers & Mathematics with Applications, vol. 56, no. 7, pp. 1773–1778, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. Yu, K. Zhang, and S. Fei, “Further results on mean square exponential stability of uncertain stochastic delayed neural networks,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 4, pp. 1582–1589, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
- Ju H. Park and O. M. Kwon, “Synchronization of neural networks of neutral type with stochastic perturbation,” Modern Physics Letters B, vol. 23, no. 14, pp. 1743–1751, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- Ju H. Park and O. M. Kwon, “Analysis on global stability of stochastic neural networks of neutral type,” Modern Physics Letters B, vol. 22, no. 32, pp. 3159–3170, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Y. Wang, Z. Wang, and J. Liang, “A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances,” Physics Letters A, vol. 372, no. 39, pp. 6066–6073, 2008. View at Publisher · View at Google Scholar · View at Scopus
- Z. Wang, H. Shu, J. Fang, and X. Liu, “Robust stability for stochastic Hopfield neural networks with time delays,” Nonlinear Analysis: Real World Applications, vol. 7, no. 5, pp. 1119–1128, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Z. Wang, Y. Liu, L. Yu, and X. Liu, “Exponential stability of delayed recurrent neural networks with Markovian jumping parameters,” Physics Letters A, vol. 356, no. 4-5, pp. 346–352, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
- Y. Liu, Z. Wang, J. Liang, and X. Liu, “Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-dependent time delays,” IEEE Transactions on Neural Networks, vol. 20, no. 7, pp. 1102–1116, 2009. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
- Z. Wang, Y. Liu, and X. Liu, “State estimation for jumping recurrent neural networks with discrete and distributed delays,” Neural Networks, vol. 22, no. 1, pp. 41–48, 2009. View at Publisher · View at Google Scholar · View at PubMed · View at Scopus
- W. Yu, “Passivity analysis for dynamic multilayer neuro identifier,” IEEE Transactions on Circuits and Systems, vol. 50, no. 1, pp. 173–178, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
- C. Li, H. Zhang, and X. Liao, “Passivity and passification of fuzzy systems with time delays,” Computers & Mathematics with Applications, vol. 52, no. 6-7, pp. 1067–1078, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- H. Gao, T. Chen, and T. Chai, “Passivity and passification for networked control systems,” SIAM Journal on Control and Optimization, vol. 46, no. 4, pp. 1299–1322, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. Zhao and D. J. Hill, “A notion of passivity for switched systems with state-dependent switching,” Journal of Control Theory and Applications, vol. 4, no. 1, pp. 70–75, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- W. Gui, B. Liu, and Z. Tang, “A delay-dependent passivity criterion of linear neutral delay systems,” Journal of Control Theory and Applications, vol. 4, no. 2, pp. 201–206, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
- W. Yu and X. Li, “Passivity analysis of dynamic neural networks with different time-scales,” Neural Processing Letters, vol. 25, no. 2, pp. 143–155, 2007. View at Publisher · View at Google Scholar · View at Scopus
- C. Li and X. Liao, “Passivity analysis of neural networks with time delay,” IEEE Transactions on Circuits and Systems II, vol. 52, no. 8, pp. 471–475, 2005. View at Publisher · View at Google Scholar · View at Scopus
- Ju H. Park, “Further results on passivity analysis of delayed cellular neural networks,” Chaos, Solitons & Fractals, vol. 34, no. 5, pp. 1546–1551, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- X. Lou and B. Cui, “Passivity analysis of integro-differential neural networks with time-varying delays,” Neurocomputing, vol. 70, no. 4–6, pp. 1071–1078, 2007. View at Publisher · View at Google Scholar · View at Scopus
- B. Chen, H. Li, C. Lin, and Q. Zhou, “Passivity analysis for uncertain neural networks with discrete and distributed time-varying delays,” Physics Letters A, vol. 373, no. 14, pp. 1242–1248, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
- X. Lou and B. Cui, “On passivity analysis of stochastic delayed neural networks with random abrupt changes,” New Mathematics and Natural Computation, vol. 3, no. 3, pp. 321–330, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- Q. Song, J. Liang, and Z. Wang, “Passivity analysis of discrete-time stochastic neural networks with time-varying delays,” Neurocomputing, vol. 72, no. 7–9, pp. 1782–1788, 2009. View at Publisher · View at Google Scholar · View at Scopus
- Q. Song and J. Cao, “Global dissipativity analysis on uncertain neural networks with mixed time-varying delays,” Chaos, vol. 18, no. 4, Article ID 043126, 10 pages, 2008. View at Publisher · View at Google Scholar · View at PubMed · View at MathSciNet