On Popov-type stability criteria for neural networks

V. Rasvan, University of Craiova, Craiova, Romania
D. Danciu, University of Craiova, Craiova, Romania

E. J. Qualitative Theory of Diff. Equ., Proc. 6'th Coll. Qualitative Theory of Diff. Equ., No. 23. (2000), pp. 1-10.

Communicated by E. Litsyn. Appeared on 2000-01-01

Abstract: This note presents some improvement of the stability criteria for continuous-time neural networks. It is taken into account that the nonlinear functions are bounded and slope restricted. This information allows application of some earlier results of Halanay and Rasvan (Int. J. Syst. Sci., 1991) on systems with slope restricted nonlinearities thus improving the results of Noldus et. al (Int. J. Syst. Sci., 1994) and also application of the results of Gelig (Avtom. i Telemekh., 1969) on systems with bounded nonlinearities. In this way a new frequency domain criterion for dichotomy and other qualitative behavior is obtained for a system with several equilibria.

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