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On the Absolute Exponential Stability of Neural Networks with Globally Lipschitz Continuous Activation Functions
Xue-Bin LIANG Toru YAMAGUCHI
IEICE TRANSACTIONS on Information and Systems
Publication Date: 1997/06/25
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Bio-Cybernetics and Neurocomputing
neural networks, absolute exponential stability, time constant, global exponential convergence rate,
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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.