Necessary and Sufficient Condition for Absolute Exponential Stability of Hopfield-Type Neural Networks


IEICE TRANSACTIONS on Information and Systems   Vol.E79-D   No.7   pp.990-993
Publication Date: 1996/07/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Bio-Cybernetics and Neurocomputing
Hopfield-type neural networks,  absolute exponential stability,  necessary and sufficient condition,  optimization,  

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A main result in this paper is that for a Hopfield-type 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.