Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis
Qi, H. and Qi, L. (2004) Deriving sufficient conditions for global asymptotic stability of delayed neural networks via nonsmooth analysis. IEEE Transactions on Neural Networks, 15, (1), 99-109. (doi:10.1109/TNN.2003.820836).
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In this paper, we obtain new sufficient conditions ensuring existence, uniqueness, and global asymptotic stability (GAS) of the equilibrium point for a general class of delayed neural networks (DNNs) via nonsmooth analysis, which makes full use of the Lipschitz property of functions defining DNNs. Based on this new tool of nonsmooth analysis, we first obtain a couple of general results concerning the existence and uniqueness of the equilibrium point. Then those results are applied to show that existence assumptions on the equilibrium point in some existing sufficient conditions ensuring GAS are actually unnecessary; and some strong assumptions such as the boundedness of activation functions in some other existing sufficient conditions can be actually dropped. Finally, we derive some new sufficient conditions which are easy to check. Comparison with some related existing results is conducted and advantages are illustrated with examples. Throughout our paper, spectral properties of the matrix (A + A/sup /spl tau//) play an important role, which is a distinguished feature from previous studies. Here, A and A/sup /spl tau// are, respectively, the feedback and the delayed feedback matrix defining the neural network under consideration.
|Digital Object Identifier (DOI):||doi:10.1109/TNN.2003.820836|
|Subjects:||Q Science > QA Mathematics > QA75 Electronic computers. Computer science|
|Divisions:||University Structure - Pre August 2011 > School of Mathematics > Operational Research
|Date Deposited:||12 May 2006|
|Last Modified:||06 Aug 2015 02:30|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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