On the Absolute Exponential Stability of Neural Networks with Globally Lipschitz Continuous Activation Functions

Xue-Bin LIANG  Toru YAMAGUCHI  

Publication
IEICE TRANSACTIONS on Information and Systems   Vol.E80-D   No.6   pp.687-690
Publication Date: 1997/06/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Bio-Cybernetics and Neurocomputing
Keyword: 
neural networks,  absolute exponential stability,  time constant,  global exponential convergence rate,  

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Summary: 
In this letter, we obtain the absolute exponential stability result of neural networks with globally Lipschitz continuous, increasing and bounded activation functions under a sufficient condition which can unify some relevant sufficient ones for absolute stability in the literature. The obtained absolute exponential stability result generalizes the existing ones about absolute stability of neural networks. Moreover, it is demonstrated, by a mathematically rigorous proof, that the network time constant is inversely proportional to the global exponential convergence rate of the network trajectories to the unique equilibrium. A numerical simulation example is also presented to illustrate the analysis results.