Title :
A simple proof of a necessary and sufficient condition for absolute stability of symmetric neural networks
Author :
Liang, Xue-Bin ; Wu, Li-De
Author_Institution :
Dept. of Comput. Sci., Fudan Univ., Shanghai, China
fDate :
9/1/1998 12:00:00 AM
Abstract :
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
Keywords :
Hopfield neural nets; absolute stability; Hopfield type; absolute stability; algebraic properties; negative semidefiniteness; neural circuit; real symmetric matrices; symmetric connection matrix; symmetric neural networks; total stability result; Asymptotic stability; Circuit stability; Computer science; Differential equations; H infinity control; Hopfield neural networks; Neural networks; Sufficient conditions; Symmetric matrices;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
