Robust stability of nonlinear time-delay systems with applications to neural networks

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

Volumn 43, Issue 7, 1996, Pages 532-543

  Ye, Hui ^a   Michel, Anthony N ^a   Wang, Kaining ^a  

^a University of Notre Dame   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; MATRIX ALGEBRA; NEURAL NETWORKS; NONLINEAR SYSTEMS; PERTURBATION TECHNIQUES; ROBUSTNESS (CONTROL SYSTEMS); STABILITY CRITERIA; SYSTEM STABILITY;

NONLINEAR TIME DELAY SYSTEMS; TIME DELAY NEURAL NETWORKS;

DELAY CIRCUITS;

EID: 0030190617     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.508172     Document Type: Article

References (28)

1. J. J. Hopfield, "Neurons with graded response have collective computational properties like those of two-state neurons," in Proc. Nai. Acad. Sei.. USA, 1984, vol. 81, pp. 3088-3092
2. J. H. Li, A. N. Michel, and W. Porod, "Qualitative analysis and synthesis of a class of neural networks." IEEE Trans. Circuits Syst., vol. 35. pp. 976-986, Aug. 1988
3. A. N. Michel, J. A. Farrell. and \V. Porod, "Qualitative theory of neural networks," IEEE Trans. Circuits Syst., vol. 36, pp. 229-243, Feb. 1989
4. J. H. Li, A. N. Michel, and W. Porod, "Analysis and synthesis of a class of neural networks: Linear systems operating on a closed hypercubc," IEEE 'Irans. Circuits Syst., vol. 36. pp. 1405 -1422, Nov. 1989
5. A. K. Michel and J. A, Farrell. "Associative memories via artificial neural networks," IEEE Control Svsl. Mag., vol. 10. no. 2, pp. 6-17, 1990
6. K. Matsuoka, "Stability conditions for nonlinear continuous neural networks with asymmetric connection weights," Neural Networks, vol. 5, pp. 495-500, 1992
7. D. G. Kelly, "Stability in contractive nonlinear neural networks," IEEE Trans. Biomed. Eng., vol. 37, 231-242, 1990
8. A. N. Michel and K. Wang, "Stability of interconnected systems: Results without quasimonotonicity conditions," in Proc. 1994 Amer. Contr. Con/, vol. 2. pp. 1781-1785
9. K. Wang and A. N. Michel, "Lyapunov stability of dynamical systems determined by differential inequalilies wilh applications lo robust stability," in Proc. 12th World Congress. Int. Federation of Automat. Conlr. 1993. vol. 4, pp. 359-363
10. __, "On Lyapunov stability of a family of nonlinear time varying systems," in Proc. 33rd IEEE Conf. Decision Contr., Bucna Vista, FL 1994. pp. 2131-2136
11. E. Chères, Z. L. Palmor. and S. Gutman, "Quantitative measures of robustness for systems including delayed perturbations," IEEE Trans Automat. Contr., vol. 34, pp. 1203-1204, 1989
12. K. K. Shyu and J. J. Yan. "Robust stability of uncertain time-dela systems and its stabilization by variable structure control," Int. J. Contr. vol. 57, no. 1, pp. 237-246. 1993.
13. H. Trinh and M. Aldeen, "On the stability of linear systems with delaye perturbations." IEEE Trans. Automal. Contr., to be published.
14. L.-M. Li, "Stability of linear neutral delay-differential systems." Bull Austral. Math. Soc., vol. 38, pp. 339-344, 1988.
15. K. Gopalsamy, Stability and Oscillations in Delay Differential Equation (if Population Dynamics. Boston, MA: Kluwer Academic, 1992, pp 436 447.
16. D. Ya. Khusainov and E. A. Yun'kova, "Estimation of magnitud of retardation in linear differential systems with deviated argument, Ukrainskii Matematicheskii Ahurnal, vol. 35, no. 2, pp. 261-264, 1981.
17. E. F. Infante, "A Lyapunov functional for a matrix difference-differentia equation," J. Differen. Equations, vol. 29, pp. 439-451, 1978.
18. J. Hale, Theory of Functional Differential Equations. New York Springer-Verlag, 1977.
19. Y. Kuang. Delay Differential Equations With Applications in Populatio Dynamics. New York: Academic. 1993.
20. C. M. Marcus and R. M. Westeivelt. "Stability of analog neural network with delay," Physical Rev. A. vol. 39, pp. 347-359, 1989.
21. T. A. Burton, "Averaged neural networks," Neural Networks, vol. 6. pp 677-680, 1993.
22. P. F. Civaüeri. M. üilli, and L. Pandolfi, "On stability of cellular neura networks with delay," IEEE Trans. Circuits Syst. I, vol. 40, pp. 157-165 1993
23. T. Roska, C. Wu, and L. O. Chua, "Stability of cellular neural networks with dominant nonlineai and delay-type templates." IEEE Trans Circuits Svst. 1, vol. 40, pp. 270-272, 1993.
24. T. Roska/C. Wu, M. Balsi, and L. O. Chua, "Stability and dynamics o delay-type general and cellular neural networks," IEEE Trans. Circuit Syst. I, vol. 39. pp. 487-490, 1992.
25. M. Gilli, "Stability of cellular neural networks and delayed cellula neural networks with nonpositive templates and nonmonotonic outpu functions," IEEE Trans. Circuits Syst. I, vol. 41, pp. 518-528, 1994.
26. H. Ye, A. N. Michel, and K. Wang, "Global stability and local stabilit of Hopfield neural networks with delays," Physical Rev. E, vol. 50, no 5, pp. 4208215, Nov. 1994.
27. __, "Qualitative analysis of Cohen-Grossberg neural networks wit multiple delays," Physical Rev. E, vol. 51. no. 3, pp. 2611-2618, Mar 1995.
28. R. K. Miller and A. N. Michel, Ordinary Differential Equations. Ne York: Academic. 1982.