A simple proof of a necessary and sufficient condition for absolutestability of symmetric neural networks
Xue-Bin Liang; Li-De Wu
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
Volume 45, Issue 9, Sep 1998 Page(s):1010 - 1011
Digital Object Identifier   10.1109/81.721271
Summary:The main result that for a neural circuit of the Hopfield type with a symmetric connection matrix T, the negative semidefiniteness of T is a necessary and sufficient condition for absolute stability was obtained and proved by rather complex procedures by Forti et al. [1994]. This brief gives a very simple proof of this result, using only the well-known total stability result about Hopfield type neural circuits with a symmetric connection matrix and the basic algebraic properties of real symmetric matrices

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