Robust stability of a class of neural networks with time delays

Journal of Dynamics and Differential Equations

Volumn 9, Issue 1, 1997, Pages 67-91

  Kharitonov, V L ^a   Paice, A D B ^b  

^a ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF BREMEN   (Germany)

Author keywords

Hopfield neural networks; Robust stability; Time delays

Indexed keywords

EID: 0009189763     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/BF02219053     Document Type: Article

References (16)

1. B. R. Barmish. New Tools for Robustness of Linear Systems, Macmillan, New York, 1994.
2. A. C. Bartlett, C. V. Hollot, and H. Lin. Root location of an entire polytope of polynomials: It suffices to check the edges. Math. Control Signals Syst. 1, 61-71, 1988.
3. J. Belair. Stability in a model of a delayed neural network. J. Dynam. Diff. Eq. 5(4), 607-623, 1993.
4. R. Bellman and K. L. Cook. Differential-Difference Equations, Academic Press, New York, 1963.
5. M. Fu, A. W. Olbrot, and M. P. Polis. Robust stability for time-delay systems: The edge theorem and graphical tests. IEEE Trans. AC-34, 813-820, 1989.
6. A. Guez, P. Protopopsecu, and J. Barhen. On the stability, storage capacity and design of nonlinear continuous neural networks. IEEE Trans. Syst. Man Cybernet. 18(1), 80-87, 1988.
7. D. Hinrichsen and A. J. Pritchard. Real and complex stability radii: A survey. In D. Hinrichsen and B. Mårtensson (eds.), Control of Uncertain Systems, Birkhauser, Boston, 1990, pp. 119-162.
8. J. J. Hopfield. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. 81 May, 3088-3092, 1984.
9. V. L. Kharitonov and A. P. Zhabko. Robust stability of time-delay systems. IEEE Trans. AC-39, 2388-2397, 1994.
10. C. M. Marcus and R. M. Westervelt. Stability of analog neural networks with delay. Phys. Rev. A 39, 347-359, 1989.
11. B. Morton and R. MacAfoos. A mu-test for real-parameter variations. Proc. Am. Control Conf, pp. 135-138, 1985.
12. A. Packard and J. C. Doyle. The complex structured singular value. Automatica 29(1), 71-109, 1993.
13. L. S. Pontryagin. On zeros of some elementary transcendental functions. Trans. AMS Ser. 2 1, 95-100, 1955.
14. L. Qui, B. Bernhardsson, A. Rantzer, E. J. Davison, P. M. Young, and J. C. Doyle. On the real structured stability radius. Proc. 32nd CDC, 1993.
15. E. D. Sontag. Neural networks for control. ECC '93 Book, 1993.
16. N. G. Tchebotareff and N. N. Meimann. The Routh-Hurwitz problem for polynomials and entire functions. Proc. Math. Inst. Acad. Sci. USSR, 1949 (in Russian).