Globally asymptotical stability of discrete-time analog neural networks

IEEE Transactions on Neural Networks

Volumn 7, Issue 4, 1996, Pages 1024-1031

  Jin, Liang ^a   Gupta, Madan M ^b  

^a SED Systems Inc   (Canada)

^b UNIVERSITY OF SASKATCHEWAN   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; DISCRETE TIME CONTROL SYSTEMS; LINEARIZATION; LYAPUNOV METHODS; MATRIX ALGEBRA; STABILITY CRITERIA; SYSTEM STABILITY;

DIAGONAL LYAPUNOV FUNCTION; DIAGONAL STABILITY; DISCRETE TIME ANALOG NEURAL NETWORKS; GLOBAL STABILITY; NETWORK PARAMETERS; SCHUR STABILITY;

NEURAL NETWORKS;

EID: 0030193060     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.508944     Document Type: Article

References (23)

1. G. Avitabile, M. Forti, S. Manetti, and M. Marini, "On a class of nonsymmetrical neural networks with application to ADC," IEEE Trans. Circuits Syst., vol. 38, pp. 202-209, Feb. 1991,
2. G. P. Barker, A. Berman, and R. Plemmons, "Positive diagonal solutions to the Lyapunov equations," Linear Multilinear Algebra, vol. 5, pp. 249-256, 1978.
3. S. P. Bhattacharyya, Robust Stabilization Against Structured Perturbations. Berlin: Springer-Verlag, 1987.
4. 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.
5. A. Guez, V. Protopopsecu, and J. Barhen, "On the stability, storage capacity, and design of nonlinear continuous neural networks," IEEE Trans. Syst., Man, Cybern., vol. SMC-18, pp. 80-87, 1988.
6. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra. New York: Academic, 1974.
7. M. W. Hirsch, "Convergent activation dynamics in continuous time networks," Neural Networks, vol. 1, pp. 331-349, May 1989.
8. J. Hopfield, "Neural networks and physical systems with emergent collective computational abilities," in Proc. Nat. Acad. Sci. USA, 1982, vol. 79, pp. 2554-2558.
9. _, "Neurons with graded response have collective computational properties like those of two state neurons," in Proc. Nat. Acad. Sci. USA, 1984, vol. 81, pp. 3088-3092.
10. R. A. Horn and C. A. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
11. L. Jin, P. N. Nikiforuk, and M. M. Gupta, "Dynamics and stability of multilayered recurrent neural networks," in Proc. 1993 IEEE Int. Conf. Neural Networks (ICNN'93), 1993, vol. II, pp. 1135-1140.
12. _, "Equilibrium stability of discrete-time dynamic neural model," in Proc. 1993 World Congr. Neural Networks, 1993, vol. IV, pp. 276-279.
13. _, "Absolute stability conditions for discrete-time recurrent neural networks," IEEE Trans. Neural Networks, vol. 5, pp. 945-955, 1994.
14. E. Kaszkurewicz and A. Bhaya, "Robust stability and diagonal Liapunov functions," SIAM J. Matrix Anal. Appl., vol. 14, no. 2. pp. 508-520, Apr. 1993.
15. D. G. Kelly, "Stability in contractive nonlinear neural networks," IEEE Trans. Biomed. Eng., vol. 37, pp. 231-242, 1990.
16. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
17. L. K. Li, "Fixed point analysis for discrete-time recurrent neural networks," Proc. IJCNN, vol. IV, pp. 134-139, June 1992.
18. D. Liu and A. N. Michel, "Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters," IEEE Trans. Circuits Syst. I, vol. 39, pp. 798-807, Oct. 1992.
19. C. M. Marcus and R. M. Westervelt, "Dynamics of iterated map neural networks," Phys. Rev. A, vol. 40, no. 1, pp. 577-587, 1989.
20. K. Matsuoka, "Stability conditions for nonlinear continuous neural networks with asymmetric connection weights," Neural Networks, vol. 5, pp. 495-500, 1992.
21. A. N. Michel and R. K. Miller, Qualitative Analysis of Large Scale Dynamical Systems. New York: Academic, 1977.
22. S. K. Persidskii, "Problem of absolute stability," Automat. Remote Contr., vol. 12, pp. 1889-1895, 1969.
23. H. Yang and T. S. Dillon, "Exponential stability and oscillation of Hopfield graded response neural networks," IEEE Trans. Neural Networks, vol. 5, pp. 719-729, 1994.