IEEEXplore# Comments on “New conditions for global stability of neural networks with application to linear and quadratic programming problems”

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Comments on “New conditions for global stability of neural networks with application to linear and quadratic programming problems”

Xue-Bin Liang Li-De Wu
Dept. of Comput. Sci., Fudan Univ., Shanghai, China;
This paper appears in: Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Publication Date: Nov. 1997
Volume: 44 , Issue: 11
On page(s): 1099 - 1101
ISSN: 1057-7122
Digital Object Identifier: 10.1109/81.641813
Current Version Published: 2002-08-06

Abstract
For original paper, see M. Forti and A. Tesi, ibid., vol. 42, pp. 354-66 (1995). This letter makes the following comments: 1) the assumption of all neuron activation functions to vanish at the origin, which is utilized in the proof of the result implying the existence and uniqueness of the network equilibrium point, can be actually omitted; 2) in the infinite sector case, the result of global asymptotic stability (GAS) remains true with respect to the class of increasing (not necessarily strictly) activations, as in the finite sector case. Consequently, a result about absolute stability (ABST) of neural networks, which can represent a generalization of the existing related ones, is also obtained

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