Synchronization for coupled neural networks with interval delay: A novel augmented Lyapunov-Krasovskii functional method

IEEE Transactions on Neural Networks and Learning Systems

Volumn 24, Issue 1, 2013, Pages 58-70

  Zhang, Huaguang ^a,b   Gong, Dawei ^a   Chen, Bing ^c   Liu, Zhenwei ^a  

^a NORTHEASTERN UNIVERSITY   (China)

^b STATE KEY LABORATORY OF SYNTHETICAL AUTOMATION FOR PROCESS INDUSTRIES   (China)

^c QINGDAO UNIVERSITY   (China)

Author keywords

Array of neural networks; Augmented Lyapunov Krasovskii functional (LKF); Hybrid coupling; Interval time varying delay; Kronecker product; Synchronization

Indexed keywords

CONSERVATIVE SYNCHRONIZATION; COUPLED NEURAL NETWORKS; DELAY-DEPENDENT SYNCHRONIZATION CRITERION; HYBRID COUPLINGS; INTERVAL TIME-VARYING DELAYS; KRONECKER PRODUCT; LYAPUNOV-KRASOVSKII FUNCTIONAL (LKF); LYAPUNOV-KRASOVSKII FUNCTIONAL METHOD;

LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NEURAL NETWORKS; TIME VARYING CONTROL SYSTEMS;

SYNCHRONIZATION;

ALGORITHM; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; FEEDBACK SYSTEM; SIGNAL PROCESSING; THEORETICAL MODEL; TIME; UNCERTAINTY;

ALGORITHMS; COMPUTER SIMULATION; FEEDBACK; MODELS, THEORETICAL; NEURAL NETWORKS (COMPUTER); SIGNAL PROCESSING, COMPUTER-ASSISTED; TIME FACTORS; UNCERTAINTY;

EID: 84880153204     PISSN: 2162237X     EISSN: 21622388     Source Type: Journal    
DOI: 10.1109/TNNLS.2012.2225444     Document Type: Article

References (34)

1. S. S. Young, P. D. Scott, and N. M. Nasrabadi, "Object recognition using multilayer Hopfield neural network," IEEE Trans. Image Process., vol. 6, no. 3, pp. 357-372, Mar. 1997.
2. T. Nishikawa, Y. C. Lai, and F. C. Hoppensteadt, "Capacity of oscillatory associative-memory networks with error-free retrieval," Phys. Rev. Lett., vol. 92, no. 10, pp. 108-101, Mar. 2004.
3. A. Georgieva and I. Jordanov, "Intelligent visual recognition and classification of cork tiles with neural networks," IEEE Trans. Neural Netw., vol. 20, no. 4, pp. 675-685, Apr. 2009.
4. S. Mishra, C. N. Bhende, and B. K. Panigrahi, "Detection and classification of power quality disturbances using S-transform and probabilistic neural network," IEEE Trans. Power Delivery, vol. 23, no. 1, pp. 280-287, Jan. 2008.
5. Y. Xia and J. Wang, "A general projection neural network for solving monotone variational inequalities and related optimization problems," IEEE Trans. Neural Netw., vol. 15, no. 2, pp. 318-328, Mar. 2004.
6. J. Zhou, S. Xu, B. Zhang, Y. Zou, and H. Shen, "Global stability of complex-valued recurrent neural networks with time-delays," IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 6, pp. 853-865, Jun. 2012.
7. J. Hu and J. Wang, "Robust exponential stability of uncertain stochastic neural networks with distributed delays and reaction-diffusions, " IEEE Trans. Neural Netw. Learn. Syst., vol. 23, no. 9, pp. 1407-1416, Sep. 2012.
8. W. Yu, J. Cao, and G. Chen, "Stability and Hopf bifurcation of a general delayed recurrent neural network," IEEE Trans. Neural Netw., vol. 19, no. 5, pp. 845-854, May 2008. (Pubitemid 351728820)
9. X. Liao, Z. Wu, and J. Yu, "Stability switches and bifurcation analysis of a neural network with continuously delay," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 29, no. 6, pp. 692-696, Nov. 1999.
10. L. Wang and X. Zou, "Capacity of stable periodic solutions in discrete-time bidirectional associative memory neural networks," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 51, no. 6, pp. 315-319, Jun. 2004.
11. C. W. Wu and L. O. Chua, "Application of graph theory to the synchronization in an array of coupled nonlinear oscillators," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 42, no. 8, pp. 494-497, Aug. 1995.
12. J. Cao, P. Li, and W. Wang, "Global synchronization in arrays of delayed neural networks with constant and delayed coupling," Phys. Lett. A, vol. 353, no. 4, pp. 318-325, May 2006. (Pubitemid 43575139)
13. J. Q. Lu, D. W. C. Ho, and M. Liu, "Globally exponential synchronization in an array of asymmetric coupled neural networks," Phys. Lett. A, vol. 369, nos. 5-6, pp. 444-451, 2007.
14. B. De Vries and J. C. Principe, "The gamma model - A new neural model for temporal processing," Neural Netw., vol. 5, no. 4, pp. 565- 576, Jul.-Aug. 1992.
15. D. W. Tank and J. J. Hopfield, "Neural computation by concentrating information in time," Proc. Nat. Acad. Sci. USA, vol. 84, no. 7, pp. 1896-1900, Apr. 1987.
16. S. G. Ruan and R. S. Filfil, "Dynamics of a two-neuron system with discrete and distributed delays," Phys. D, vol. 191, nos. 3-4, pp. 323-342, May 2004.
17. Y. R. Liu, Z. D. Wang, and X. H. Liu, "Global exponential stability of generalized recurrent neural networks with discrete and distributed delays," Neural Netw., vol. 19, no. 5, pp. 667-675, Jun. 2006.
18. J. Cao, G. Chen, and P. Li, "Global synchronization in an array of delayed neural networks with hybrid coupling," IEEE Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 2, pp. 488-498, Apr. 2008. (Pubitemid 351479567)
19. J. Cao and L. Li, "Cluster synchronization in an array of hybrid coupled neural networks with delay," Neural Netw., vol. 22, no. 2, pp. 335-342, 2009.
20. X. F. Wang and G. Chen, "Synchronization in scale-free dynamical networks: Robustness and fragility," IEEE Trans. Circuit Syst. I, Reg. Papers, vol. 49, no. 1, pp. 54-62, Jan. 2002. (Pubitemid 34231903)
21. Z. Li and G. Chen, "Global synchronization and asymptotic stability of complex dynamical networks," IEEE Trans. Circuit Syst. II, Exp. Briefs, vol. 53, no. 1, pp. 28-33, Jan. 2006. (Pubitemid 46511147)
22. J. Zhou and T. Chen, "Synchronization in general complex delayed dynamical networks," IEEE Trans. Circuit Syst. I, Reg. Papers, vol. 53, no. 3, pp. 733-744, Mar. 2006.
23. Y. Zhang, S. Xu, Y. Chu, and J. Lu, "Robust global synchronization of complex networks with neutral-type delayed nodes," Appl. Math. Comput., vol. 216, no. 3, pp. 768-778, Apr. 2010.
24. K. Yuan, "Robust synchronization in arrays of coupled networks with delay and mixed coupling," Neurocomputing, vol. 72, nos. 4-6, pp. 1026-1031, Jan. 2009.
25. M. Yang, Y. Wang, J. Xiao, and H. O. Wang, "Robust synchronization of impulsively-coupled complex switched networks with parametric uncertainties and time-varying delays," Nonlinear Anal., Real World Appl., vol. 11, no. 4, pp. 3008-3020, Aug. 2010.
26. K. Gu, V. Kharitonov, and J. Chen, Stability of Time-Delay Systems. Boston, MA: Birkhäuser, 2003.
27. H. Zhang, Z. Liu, G. Huang, and Z. Wang, "Novel weighting-delay- based stability criteria for recurrent neural networks with time-varying delay," IEEE Trans. Neural Netw., vol. 21, no. 1, pp. 91-106, Jan. 2010.
28. 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 Trans. Syst., Man, Cybern. B, Cybern., vol. 38, no. 5, pp. 1314-1325, Oct. 2008.
29. I. R. Petersen and C. V. Hollot, "A Riccati equation approach to the stabilization of uncertain linear systems," Automatica, vol. 22, no. 4, pp. 397-411, Jul. 1986.
30. Y. Liu, Z. Wang, and X. Liu, "Design of exponential state estimators for neural networks with mixed time delays," Phys. Lett. A, vol. 364, pp. 401-412, May 2007.
31. Z. Wang, Y. Liu, and X. Liu, "On global asymptotic stability of neural networks with discrete and distributed delays," Phys. Lett. A, vol. 345, nos. 4-6, pp. 299-308, Oct. 2005. (Pubitemid 41262382)
32. Z. Wang, H. Shu, Y. Liu, D. Ho, and X. Liu, "Robust stability analysis of generalized neural networks with discrete and distributed time delays," Chaos, Solitons Fractals, vol. 30, no. 4, pp. 886-896, Nov. 2006.
33. Y. Liu, Z. Wang, and X. Liu, "Global exponential stability of generalized recurrent neural networks with discrete and distributed delays," Neural Netw., vol. 19, no. 5, pp. 667-675, Jun. 2006.
34. Y. Liu, Z.Wang, and X. Liu, "Robust stability of discrete-time stochastic neural networks with time-varying delays," Neurocomputing, vol. 71, nos. 4-6, pp. 823-833, Jan. 2008. (Pubitemid 351168431)