Novel weighting-delay-based stability criteria for recurrent neural networks with time-varying delay

IEEE Transactions on Neural Networks

Volumn 21, Issue 1, 2010, Pages 91-106

  Zhang, Huaguang ^a   Liu, Zhenwei ^a   Huang, Guang Bin ^b   Wang, Zhanshan ^a  

^a NORTHEASTERN UNIVERSITY   (China)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

Delay dependent stability; Recurrent neural networks (RNNs); Time varying delay; Weighting delay

Indexed keywords

DELAY DEPENDENT STABILITY CRITERION; DELAY PARAMETERS; DELAY-DEPENDENT STABILITY; OPTIMAL WEIGHTING; OPTIMIZATION METHOD; STABILITY MARGINS; STABILITY PROBLEM; SUBINTERVALS; TIME-VARYING DELAY;

STABILITY CRITERIA; SYSTEM STABILITY; THREE TERM CONTROL SYSTEMS; TIME VARYING CONTROL SYSTEMS; TIME VARYING NETWORKS; WEIGHING;

RECURRENT NEURAL NETWORKS;

ALGORITHM; ARTICLE; ARTIFICIAL NEURAL NETWORK; COMPUTER SIMULATION; FEEDBACK SYSTEM; NONLINEAR SYSTEM; RECURRENT DISEASE; STATISTICAL MODEL; TIME;

ALGORITHMS; COMPUTER SIMULATION; FEEDBACK; MODELS, STATISTICAL; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; RECURRENCE; TIME FACTORS;

EID: 73949132376     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNN.2009.2034742     Document Type: Article

References (37)

1. L. O. Chua and L. Yang, "Cellular neural networks: Applications," IEEE Trans. Circuits Syst., vol. CAS-35, no. 10, pp. 1273-1290, Oct. 1988.
2. T. Roska and L. O. Chua, "Cellular neural networks with non-linear and delay-type template elements and non-uniform grids," Int. J. Circuit Theory Appl., vol. 20, no. 5, pp. 469-481, 1992.
3. Y. H. Chen and S. C. Fang, "Neurocomputing with time delay analysis for solving convex quadratic programming problems," IEEE Trans. Neural Netw., vol. 11, no. 1, pp. 230-240, Jan. 2000.
4. 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.
5. R. Fantacci, M. Forti, M. Marini, and L. Pancani, "Cellular neural networks approach to a class of communication problems," IEEE Trans. Circuits Syst. I, Fund. Theory Appl., vol. 46, no. 12, pp. 1457-1467, Dec. 1999. (Pubitemid 30558662)
6. J. A. Farrell and A. N. Michel, "A synthesis procedure for Hopfield's continuous-time associative memory," IEEE Trans. Circuits Syst., vol. 37, no. 7, pp. 877-884, Jul. 1990.
7. A. N. Michel, J. A. Farrell, and H. F. Sun, "Analysis and synthesis techniques for Hopfield type synchronous discrete-time neural networks with applications to associative memory," IEEE Trans. Circuits Syst., vol. 37, no. 11, pp. 1356-1366, Nov. 1990.
8. 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.
9. D. L. Wang, "Emergent synchrony in locally coupled neural oscillators," IEEE Trans. Neural Netw., vol. 6, no. 4, pp. 941-948, Jul. 1995.
10. 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.
11. T. Liao and F.Wang, "Global stability for cellular neural networks with time delay," IEEE Trans. Neural Netw., vol. 11, no. 6, pp. 1481-1484, Nov. 2000.
12. S. Arik, "An analysis of global asymptotic stability of delayed neural networks," IEEE Trans. Neural Netw., vol. 13, no. 5, pp. 1239-1242, Sep. 2002.
13. S. Arik, "Global asymptotic stability of a larger class of neural networks with constant time delay," Phys. Lett. A, vol. 311, pp. 504-511, 2003.
14. V. Singh, "A generalized LMI-based approach to the global asymptotic stability of delayed cellular neural networks," IEEE Trans. Neural Netw., vol. 15, no. 1, pp. 223-225, Jan. 2004.
15. J. Cao and J.Wang, "Global asymptotic stability of a class of recurrent neural networks with time-varying delays," IEEE Trans. Circuits Syst. I, Fund. Theory Appl., vol. 50, no. 1, pp. 34-44, Jan. 2003.
16. J. Cao and J. Wang, "Global asymptotic stability and robust stability of recurrent neural networks with time delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 2, pp. 417-426, Feb. 2005. (Pubitemid 40319475)
17. J. Cao and J. Wang, "Global exponential stability and periodicity of recurrent neural networks with time delays," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 5, pp. 920-931, May 2005. (Pubitemid 40773619)
18. H. Zhang, Z. Wang, and D. Liu, "Global asymptotic stability of recurrent neural networks with multiple time-varying delays," IEEE Trans. Neural Netw., vol. 19, no. 5, pp. 855-873, May 2008. (Pubitemid 351728821)
19. H. Zhang and Z. Wang, "Global asymptotic stability of delayed cellular neural networks," IEEE Trans. Neural Netw., vol. 18, no. 3, pp. 947-950, May 2007. (Pubitemid 46773762)
20. X. Liao, G. Chen, and E. Sanchez, "Delay-dependent exponential stability analysis of delay neural networks: An LMI approach," Neural Netw., vol. 15, pp. 855-866, 2002. (Pubitemid 35299581)
21. S. Xu, J. Lam, D.Wu, and Y. Zou, "Newglobal asymptotic stability criteria for delayed cellular neural networks," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 52, no. 6, pp. 349-353, Jun. 2005.
22. C. Hua, C. Long, and X. Guan, "New results on stability analysis of neural networks with time-varying delays," Phys. Lett. A, vol. 352, pp. 335-340, 2006.
23. H. Cho and J. Park, "Novel delay-dependent robust stability criterion of delayed cellular neural networks," Chaos Solitons Fractals, vol. 32, pp. 1194-1200, 2007.
24. Y. He, M. Wu, and J. She, "Delay-dependent exponential stability of delayed neural networks with time-varying delay," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 7, pp. 553-557, Jul. 2006. (Pubitemid 44111522)
25. Y. He, G. Liu, and D. Rees, "New delay-dependent stability criteria for neural networks with time-varying delay," IEEE Trans. Neural Netw., vol. 18, no. 1, pp. 310-314, Jan. 2007.
26. Y. He, G. Liu, D. Rees, and M.Wu, "Stability Analysis for neural networks with time-varying interval delay," IEEE Trans. Neural Netw., vol. 18, no. 6, pp. 1850-1854, Nov. 2007.
27. M. Parlakçi, "Robust stability of uncertain neutral systems: A novelaugmented Lyapunov functional approach," IET Control Theory Appl., vol. 1, no. 3, pp. 802-809, May 2007.
28. C. Peng and Y. Tian, "Delay-dependent robust stability criteria for uncertain systems with interval time-varying delay," J. Comput. Appl. Math., vol. 214, no. 2, pp. 480-494, May 2008.
29. T. Li, L. Guo, C. Sun, and C. Lin, "Further result on delay-dependent stability criterion of neural networks with time-varying delays," IEEE Trans. Neural Netw., vol. 19, no. 4, pp. 726-730, Apr. 2008. (Pubitemid 351583586)
30. X. G. Li and X. J. Zhu, "Stability analysis of neutral systems with distributed delays," Automatica, vol. 44, no. 8, pp. 2197-2201, Aug. 2008.
31. E. Fridman and U. Shaked, "A descriptor system approach to H∞ control of linear time-delay systems," IEEE Trans. Autom. Control, vol. 47, no. 2, pp. 253-270, Feb. 2002. (Pubitemid 34291539)
32. S. Mou, H. Gao, J. Lam, and W. Qiang, "A new criterion of delaydependent asymptotic stability for Hopfield neural networks with time delay," IEEE Trans. Neural Netw., vol. 19, no. 3, pp. 532-535, Mar. 2008.
33. K. Gu, V. Kharitonov, and J. Chen, Stability of Time-Delay Systems. Cambridge, MA: Birkhauser, 2003.
34. M. Liu, "Delayed standard neural network model and its application," (in Chinese) ACTA Automatica Sinica, vol. 31, no. 5, pp. 750-758, 2005.
35. J. Hale, Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
36. J. A. Nelder and R. Mead, "A simplex method for function minimization," Comput. J., vol. 7, pp. 308-313, 1965.
37. P. Park and J. Ko, "Stability and robust stability for systems with a time-varying delay," Automatica, vol. 43, no. 10, pp. 1855-1858, Oct. 2007.