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Necessary and Sufficient Condition for Absolute Exponential Stability of HopfieldType Neural Networks
XueBin LIANG Toru YAMAGUCHI
Publication
IEICE TRANSACTIONS on Information and Systems
Vol.E79D
No.7
pp.990993 Publication Date: 1996/07/25
Online ISSN:
DOI:
Print ISSN: 09168532 Type of Manuscript: PAPER Category: BioCybernetics and Neurocomputing Keyword: Hopfieldtype neural networks, absolute exponential stability, necessary and sufficient condition, optimization,
Full Text: PDF(340.2KB)>>
Summary:
A main result in this paper is that for a Hopfieldtype neural circuit with a symmetric connection matrix T, the negative semidenfiniteness of T is a necessary and sufficient condition for absolute exponential stability. While this result extends one of absolute stability in Forti, et al. [1], its proof given in this paper is simpler, which is completed by an approach different from one used in Forti et al. [1]. The most significant consequence is that the class of neural networks with negative semidefinite matrices T is the largest class of symmetric networks that can be employed for embedding and solving optimization problem with global exponential rate of convergence to the optimal solution and without the risk of spurious responses.

