Necessary and sufficient condition for absolute stability of normal neural networks

Neural Networks

Volumn 16, Issue 8, 2003, Pages 1223-1227

  Chu, Tianguang ^a   Zhang, Cishen ^b   Zhang, Zongda ^c  

^a PEKING UNIVERSITY   (China)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Absolute stability; Global convergence; Lyapunov function; Neural networks; Normal connection matrix; Quasi normal matrix condition

Indexed keywords

LYAPUNOV METHODS; MATRIX ALGEBRA; STABILITY;

CONNECTION MATRICES;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; DYNAMICS; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL;

EID: 0041332889     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-6080(03)00075-3     Document Type: Article

References (21)

1. Almeida L.B. A learning rule for asynchronous perceptrons with feedback in a combinatorial environment. Proceedings of the IEEE 1st International Conference on Neural Networks. II:1987;609-618.
2. Chu T. Convergence in discrete-time neural networks with specific performance. Physical Review E. 63:2001;051904.
3. Chua L.O., Roska T. Stability of a class of nonreciprocal cellular neural networks. IEEE Transactions on Circuits and Systems. 37:1990;1520-1527.
4. Chua L.O., Yang L. Cellular neural networks: theory. IEEE Transactions on Circuits and Systems. 35:1988;1257-1272.
5. Cohen M.A., Grossberg S. Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Transactions on Systems, Man and Cybernetics. 13:1983;815-821.
6. Cosnard M., Goles E. Discrete state neural networks and energies. Neural Networks. 10:1997;327-334.
7. Forti M., Liberatore A., Manetti S., Marini M. On absolute stability of neural networks. Proceedings of 1994 IEEE International Symposium on Circuits and Systems. 6:1994;241-244.
8. Forti M., Manetti S., Marini M. Necessary and sufficient conditions for absolute stability of neural networks. IEEE Transactions on Circuits and Systems I. 41:1994;491-494.
9. Goles E., Martinez S. Mathematics and applications. Neural and automata networks mathematics and applications. Vol. 58:1990;Kluwer, Dordrecht.
10. Hahn W. Stability of motion. 1967;Springer, Berlin.
11. Hirsch M.W. Convergent activation dynamics in continuous time networks. Neural Networks. 2:1989;331-349.
12. Hopfield J.J. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Science (USA). 79:1982;2554-2558.
13. Hopfield J.J., Tank D.W. Computing with neural circuits: a model. Science. 233:1986;625-633.
14. Horn R.A., Johnson C.R. Matrix analysis. 1990;Cambridge University Press, Cambridge.
15. Kaszkurewicz E., Bhaya A. Comments on Necessary and sufficient condition for absolute stability of neural networks. IEEE Transactions on Circuits and Systems I. 42:1995;497-499.
16. Kobuchi Y. State evaluation functions and Lyapunov functions for neural networks. Neural Networks. 4:1991;505-510.
17. Liang X.-B., Yamaguchi T. Necessary and sufficient condition for absolute exponential stability of a class of nonsymmetric neural networks. IEICE Transactions on Information and Systems. E80:1997;802-807.
18. Matsuoka K. Stability conditions for nonlinear continuous neural networks with asymmetric connection weights. Neural Networks. 5:1992;495-500.
19. Michel A.N., Farrel J.A., Porod W. Qualitative analysis of neural networks. IEEE Transactions on Circuits and Systems. 36:1989;229-243.
20. Schürmann B. Stability and adaptation in artificial neural systems. Physical Review A. 40:1989;2681-2688.
21. Wu C.W., Chua L.O. A more rigorous proof of complete stability of cellular neural networks. IEEE Transactions on Circuits and Systems I. 44:1997;370-371.