Absolute exponential stability of neural networks with a general class of activation functions

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

Volumn 47, Issue 8, 2000, Pages 1258-1263

  Liang, Xue Bin ^a   Wang, Jun ^b,c  

^a FUDAN UNIVERSITY   (China)

^b UNIVERSITY OF DELAWARE   (United States)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; FUNCTIONS; LYAPUNOV METHODS; MATRIX ALGEBRA; NEURAL NETWORKS; OPTIMIZATION; THEOREM PROVING;

ABSOLUTE EXPONENTIAL STABILITY; ACTIVATION FUNCTIONS; GLOBALLY EXPONENTIALLY STABLE; INTERCONNECTION MATRIX; LIPSCHITZ FUNCTIONS;

ASYMPTOTIC STABILITY;

EID: 0034243274     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.873882     Document Type: Article

References (25)

1. M. Forti, S. Manetti, andM.Marini, "Necessary and sufficient condition for absolute stability of neural networks," IEEE Trans. Circuits Syst. I, vol. 41, pp. 491-494, 1994.
2. M. Forti, A. Liberatore, S. Manetti, and M. Marini, "On absolute stability of neural networks,"in Proc. 1994 IEEE Int. Symp. Circuit Syst., vol. 6, May 1994, pp. 241-244.
3. M. Forti, "On global asymptotic stability of a class of nonlinear system arising in neural network theory," / Differential Equations, vol. 113, pp. 246-266, Oct. 1994.
4. E. Kaszkurewicz and A. Bhaya, "On a class of globally stable neural circuits," IEEE Trans. Circuits Syst. I, vol. 41, pp. 171-174, 1994.
5. "Comments on 'Necessary and sufficient condition for absolute stability of neural networks'," IEEE Trans. Circuits Syst. I, vol. 42, pp. 497-499, 1995.
6. S. Arik and V. Tavsanoglu, "Absolute stability of nonsymmetric neural networks," in Proc. 1996 IEEE Int. Symp. Circuit Syst., vol. Ill, May 1996, pp. 441-4444.
7. "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, 1998.
8. 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, 1998.
9. M. Forti and A. Tesi, "New conditions for global stability of neural networks with application to linear and quadratic programming problems," IEEE Trans. Circuits Syst. I, vol. 42, pp. 354-366, 1995.
10. S. I. Sudharsanan and M. K. Sundareshan, "Exponential stability and a systematic synthesis of a neural network for quadratic minimization," Neural Networks, vol. 4, no. 5, pp. 599-613, 1991.
11. A. Bouzerman and T. R. Pattison, "Neural network for quadratic optimization with bound constraints, "IEEE Trans. Neural Networks, vol. 4, pp. 293-303, 1993.
12. J. J. Hopfield, "Neurons with graded response have collective computation properties like those of two-state neurons," Proc. Nat. Acad. Sci., vol. 81, no. 5, pp. 3088-3092, 1984.
13. L. O. Chua and L. Yang, "Cellular neural networks: theory," IEEE Trans. Circuits Syst., vol. 35, pp. 1257-1272, 1988.
14. J. K. Hale, Ordinary Differential Equations. New York: Wiley Intersci., 1969.
15. M. Fiedler and V. Ptâk, "Some generalizations of positive definiteness and monotonicity," Numer. Math., vol. 9, no. 2, pp. 163-172, 1966.
16. I. W. Sandberg and A. N. Willson Jr., "Some theorems on properties of dc equations of nonlinear networks," Bell Syst. Tech. J., vol. 48, no. 1, pp. 1-34, 1969.
17. A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences. New York: Academic, 1979.
18. D. Hershkowitz, "Recent directions in matrix stability," Linear Algebra Applicat., vol. 172, pp. 161-186, 1992.
19. L. O. Chua and N. N. Wang, "On the application of degree theory to the analysis of resistive nonlinear networks," Int. J. Circuit Theory Applicat., vol. 5, pp. 45-68, 1977.
20. J. Cronin, Fixed Points and Topological Degree in Nonlinear Analysis. Providence, RI: Amer. Math. Soc., 1964.
21. M. Forti, "A note on neural networks with multiple equilibrium points," IEEE Trans. Circuits Syst. I, vol. 43, pp. 487-491, 1996.
22. A. N. Michel, J. A. Farrell, and W. Porod, "Qualitative analysis of neural networks," IEEE Trans. Circuits Syst., vol. 36, pp. 229-243, 1989.
23. A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems. New York: Academic, 1977.
24. I. W. Sandberg, "Some theorems on the dynamic response of nonlinear transistor networks," Bell Syst. Tech. J., vol. 48, no. 1, pp. 35-54, 1969.
25. E. Kaszkurewicz and A. Bhaya, "Diagonal stability in the large scale system approach," Nonlinear Analysis, vol. 35, no. 1, pp. 143-152, 1999.