Global asymptotic stability of a general class of recurrent neural networks with time-varying delays

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 50, Issue 1, 2003, Pages 34-44

  Cao, Jinde ^a   Wang, Jun ^b  

^a SOUTHEAST UNIVERSITY   (China)

^b CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Equilibrium point; Global asymptotic stability; Lyapunov functional; Nonsingular M matrix; Recurrent neural networks; Time varying delays; Topological degree

Indexed keywords

ASYMPTOTIC STABILITY; LYAPUNOV METHODS; MATRIX ALGEBRA; TIME VARYING NETWORKS;

BIDIRECTIONAL ASSOCIATIVE MEMORY NETWORKS;

RECURRENT NEURAL NETWORKS;

EID: 0037216976     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2002.807494     Document Type: Article

References (39)

1. J. J. Hopfied, "Neural networks with graded response have collective computational properties like those of two-stage neurons," in Proc. Nat. Acad. Sci. USA, vol. 81, 1984, pp. 3088-3092.
2. C. M. Marcus and R. M. Westervelt, "Stability of analog neural networks with delays," Phys. Rev. A, vol. 39, no. 1, pp. 347-359, 1989.
3. P. V. D. Driessche and X. Zou, "Global attractivity in delayed Hopfield neural network models," SIAM J. Appl. Math., vol. 58, no. 6, pp. 1878-1890, 1998.
4. J. Cao and D. Zhou, "Stability analysis of delayed cellular neural networks," Neural Netw., vol. 11, pp. 1601-1605, 1998.
5. C. Hou and J. Qian, "Stability analysis for neural dynamics with time-varying delays," IEEE Trans. Neural Networks, vol. 9, pp. 221-223, Jan. 1998.
6. K. Gopalsamy and X. Z. He, "Delay-indepent stability in bidirectional associative memory networks," IEEE Trans. Neural Networks, vol. 5, pp. 998-1002, Nov. 1994.
7. H. Lu, "On stability of nonlinear continuous-time neural networks with delays," Neural Netw., vol. 13, pp. 1135-1143, 2000.
8. M. Joy, "On the global convergence of a class of functional differential equations with applications in neural network theory," J. Math. Anal. Applicat., vol. 232, pp. 61-81, 1999.
9. T. Burton, Stability and Periodic Solution of Ordinary Differential Equation and Functional Differential Equations. Orlando, FL: Academic, 1985.
10. J. K. Hale, Theory of Functional Differential Equations. New York: Springer-Verlag, 1977.
11. D. Hershknowitz, "Recent directions in matrix stability," Linear Algebra Applicat., vol. 171, pp. 161-186, 1992.
12. J. P. Moylan, "Matrices with positive principal minors," Linear Algebra Applicat., vol. 17, pp. 53-58, 1977.
13. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Science. New York: Academic, 1979.
14. J. Cronin, Fixed Points and Topological Degree in Nonlinear Analysis. Providence, RI: Amer. Math. Soc., 1964.
15. J. Cao and L. Wang, "Periodic oscillatory solution of bidirectional associative memory networks with delays," Phys. Rev. E, Stat. Phys. Plasmas Fluids Relat., vol. 61, pp. 1825-1828, 2000.
16. _, "Exponential stability and periodic oscillatory solution in BAM networks with delays," IEEE Trans. Neural Networks, vol. 13, pp. 457-463, Mar. 2002.
17. P.P. Civalleri, L. M. Gilli, and L. Pabdolfi, "On stability of cellular neural networks with delay," IEEE Trans. Circuits Syst. I, vol. 40, pp. 157-165, Mar. 1993.
18. J. Cao, "A set of stability criteria for delayed cellular neural networks," IEEE Trans. Circuits Syst. I, vol. 48, pp. 494-498, Apr. 2001.
19. C. H. Feng and R. Plamondon, "On the stability analysis of delayed neural networks systems," Neural Netw., vol. 14, pp. 1181-1188, 2001.
20. M. Gilli, "Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions," IEEE Trans. Circuits Syst. I, vol. 41, pp. 518-528, Aug. 1994.
21. T. L. Liao and F. C. Wang, "Global stability for cellular neural networks with time delay," IEEE Trans. Neural Networks, vol. 11, pp. 1481-1484, Nov. 2000.
22. J. Cao, "Global stability conditions for delayed CNNs," IEEE Trans. Circuits Syst. I, vol. 48, pp. 1330-1333, Nov. 2001.
23. T. Roska and L. O. Chua, "Cellular neural networks with nonlinear and delay-type template," Int. J. Circuit Theory Appl., vol. 20, pp. 469-481, 1992.
24. T. Roska, C. W. Wu, and L. O. Chua, "Stability of cellular neural networks with dominant nonlinear and delay-type template," IEEE Trans. Circuits Syst. I, vol. 40, pp. 270-272, Apr. 1993.
25. T. Roska, C. W. Wu, M. Balsi, and L. O. Chua, "Stability and dynamics of delay-type general and cellular neural networks," IEEE Trans. Circuits Syst. I, vol. 39, pp. 487-490, June 1992.
26. J. Cao, "Periodic oscillation and exponential stability of delayed CNNs," Phys. Lett. A, vol. 270, no. 3-4, pp. 157-163, 2000.
27. _, "Exponential stability and periodic solution of delayed cellular neural networks," Sci. China, ser. E, vol. 43, no. 3, pp. 328-336, 2000.
28. S. Arik and V. Tavsanoglu, "On the global asymptotic stability of delayed cellular neural networks," IEEE Trans. Circuits Syst. I, vol. 47, pp. 571-574, Apr. 2000.
29. J. Cao, "Global exponential stability of Hopfield neural networks," Int. J. Syst. Sci., vol. 32, no. 2, pp. 233-236, 2001.
30. J. A. Farrell and A. N. Michel, "A synthesis procedure for Hopfield's continuous-time associative memory," IEEE Trans. Circuits Syst., vol. 37, pp. 877-884, July 1990.
31. B. Kosko, "Bi-directional associative memories," IEEE Trans. Syst. Man., Cybern., vol. 18, pp. 49-60, Jan. 1988.
32. M. Forti, S. Manetti, and M. Marini, "Necessary and sufficient condition for absolute stability of neural networks," IEEE Trans. Circuits Syst. I, vol. 41, pp. 491-494, July 1994.
33. E. Kaszkurewicz and A. Bhaya, "Comments on "Necessary and sufficient condition for absolute stability of neural networks"," IEEE Trans. Circuits Syst. I, vol. 42, pp. 497-499, Aug. 1995.
34. X. B. Liang and L. D. Wu, "A comment on "Comments on necessary and sufficient condition for absolute stability of neural networks"," IEEE Trans. Circuits Syst. I, vol. 45, pp. 594-594, May 1998.
35. S. Arik and V. Tavsanoglu, "A comment on 'Comments on necessary and sufficient condition for absolute stability of neural networks'," IEEE Trans. Circuits Syst. I, vol. 45, pp. 595-596, May 1998.
36. X. B. Liang and L. D. Wu, "New sufficient conditions for absolute stability of neural networks," IEEE Trans. Circuits Syst. I, vol. 45, pp. 584-586, May 1998.
37. X. B. Liang and J. Wang, "Absolute exponential stability of neural networks with a general class of activation functions," IEEE Trans. Circuits Syst. I, vol. 47, pp. 1258-1263, Aug. 2000.
38. _, "An additive diagonal stability condition for absolute exponential stability of a general class of neural networks," IEEE Trans. Circuits Syst. I, vol. 48, pp. 1308-1317, Nov. 2001.
39. S. Arik and V. Tavsanoglu, "Absolute stability of nonsymmetric neural networks," Proc. IEEE Int. Symp. Circuits and Systems, ISCAS'96, pp. 441-444, May 1996.