Absolutely exponential stability of a class of neural networks with unbounded delay

Neural Networks

Volumn 17, Issue 3, 2004, Pages 391-397

  Zhang, Jiye ^a,b   Suda, Yoshihiro ^b   Iwasa, Takashi ^b  

^a SOUTHWEST JIAOTONG UNIVERSITY   (China)

^b UNIVERSITY OF TOKYO   (Japan)

Author keywords

Absolutely exponential stability; Neural networks; Partially Lipschitz; Unbounded delay

Indexed keywords

LYAPUNOV METHODS; MATRIX ALGEBRA; NONLINEAR SYSTEMS; SYSTEM STABILITY; VECTORS;

EXPONENTIAL STABILITY;

NEURAL NETWORKS;

ARTICLE; ARTIFICIAL NEURAL NETWORK; MATHEMATICAL ANALYSIS; NERVE CELL; PRIORITY JOURNAL; THEORY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTER SIMULATION; HUMANS; MODELS, NEUROLOGICAL; NERVE NET; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; TIME FACTORS;

EID: 1642373914     PISSN: 08936080     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neunet.2003.09.005     Document Type: Article

References (33)

1. Arik S., Tavanoglu V. Equilibrium analysis of delayed CNNs. IEEE Transactions on Circuits and Systems - I. 45:1998;168-171.
2. Arik S., Tavanoglu V. On the global asymptotic stability of delayed cellular neural networks. IEEE Transactions on Circuits and Systems - I. 47:2000;571-574.
3. Bouzerdoum A., Pattison T.R. Neural networks for quadratic optimization with bound constraints. IEEE Transactions on Neural Networks. 4:1993;293-303.
4. Cao J. A set of stability criteria for delayed cellular neural networks. IEEE Transactions on Circuits Systems - I. 48:2001;494-498.
5. Chen T. Global exponential stability of delayed Hopfield neural networks. Neural Networks. 14:2001;977-980.
6. Chen Y. Global stability of neural networks with distributed delays. Neural Networks. 15:2002;867-871.
7. Chua L.O. CNN: A paradigm for complexity. 1998;World Scientific, Singapore.
8. Chua L.O., Yang L. Cellular neural networks: theory. IEEE Transactions on Circuits Systems. 35:1988;1257-1272.
9. Chua L.O., Yang L. Cellular neural networks: applications. IEEE Transactions on Circuits Systems. 35:1988;1273-1290.
10. Civalleri P.P., Gill L.M., Pandolfi L. On stability of cellular neural networks with delay. IEEE Transactions on Circuits and Systems - I. 40:1993;157-164.
11. Feng C., Plamondon R. On the stability analysis of delayed neural networks systems. Neural Networks. 14:2001;1181-1188.
12. Fiedler M., Ptak V. Some generalizations of positive definiteness and monotonicity. Numerical Mathematics. 9:1966;163-172.
13. Forti M., Tesi A. New conditions for global stability of neural networks with application to linear and quadratic programming problems. IEEE Transactions on Circuits and Systems - I. 42:(7):1995;354-366.
14. Gopalsamy K., He X. Stability in asymmetric Hopfield nets with transmission delays. Physica D. 76:1994;344-358.
15. Joy M. On the global convergence of a class of functional differential equations with applications in neural network theory. Journal of Mathematics Analysis and Applications. 232:1999;61-81.
16. Joy M. Results concerning the absolute stability of delayed neural networks. Neural Networks. 13:2000;613-616.
17. Kennedy M.P., Chua L.O. Neural networks for nonlinear programming. IEEE Transactions on Circuits and Systems. 35:(9):1988;554-562.
18. Michel A.N., Farrell J.A., Porod W. Qualitative analysis of neural networks. IEEE Transactions on Circuits and Systems. 36:(2):1989;229-243.
19. Mohamad S. Global exponential stability in continuous time and discrete-time delayed bi-directional neural networks. Physica D. 159:2001;233-251.
20. Peng J., Qiao H., Xu Z. A new approach to stability of neural networks with time-varying delays. Neural Networks. 15:2002;95-103.
21. Roska T., Chua L.O. Cellular neural networks with delay type template elements and nonuniform grids. International Journal of Circuit Theory and Applications. 20:(4):1992;469-481.
22. Roska T., Wu C.W., Balsi M., Chua L.O. Stability of cellular neural networks with dominant nonlinear and delay-type templates. IEEE Transactions on Circuits and Systems - I. 40:1993;270-272.
23. Siljiak D.D. Large-scale dynamic systems - stability and structure. 1978;Elsevier/North-Holland, New York.
24. Sree Hari Rao V., Phaneendra B.R.M. Global dynamics of bidirectional associative memory neural networks involving transmission delays and dead zones. Neural Networks. 12:1999;455-465.
25. Van Den Driessche P., Zou X. Global attractivity in delayed Hopfield neural networks models. SIAM Journal of Applied Mathematics. 58:(6):1998;1878-1890.
26. Yi Z., Peng P.A., Leung K.S. Convergence analysis of cellular neural networks with unbounded delay. IEEE Transactions on Circuits and Systems - I. 48:2001;680-687.
27. Zhang J. Absolutely exponential stability in delayed cellular neural networks. International Journal of Circuit Theory and Applications. 30:(4):2002;395-409.
28. Zhang J. Globally exponential stability of neural networks with variable delays. IEEE Transactions on Circuits and Systems - I. 50:(2):2003;288-291.
29. Zhang J. Global stability analysis in delayed cellular neural networks. Computers and Mathematics with Applications. 45:2003;1707-1720.
30. Zhang J., Jin X. Global stability analysis in delayed Hopfield neural networks models. Neural Networks. 13:(7):2000;745-753.
31. Zhang J., Yang Y. Global stability analysis of bidirectional associative memory neural networks with time delay. International Journal of Circuit Theory and Application. 29:(2):2001;185-196.
32. Zhang J., Yang Y., Zeng J. String stability of infinite interconnected system. Applied Mathematics and Mechanics. 21:(7):2000;791-796.
33. Zhang Q., Wei X., Xu J. Global exponential stability of Hopfield neural networks with continuously distributed delays. Physics Letters A. 315:2003;431-436.