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Title: Global exponential stability of generalized recurrent neural networks with discrete and distributed delays
Authors: Liu, Y
Wang, Z
Liu, X
Keywords: Generalized recurrent neural networks
Discrete and distributed delays
Lyapunov–Krasovskii functional
Global exponential stability
Global asymptotic stability
Linear matrix inequality
Publication Date: 2006
Publisher: Elsevier
Citation: Neural Networks, 19(5): 667-675, Jun 2006
Abstract: This paper is concerned with analysis problem for the global exponential stability of a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. We first prove the existence and uniqueness of the equilibrium point under mild conditions, assuming neither differentiability nor strict monotonicity for the activation function. Then, by employing a new Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions for the RNNs to be globally exponentially stable. Therefore, the global exponential stability of the delayed RNNs can be easily checked by utilizing the numerically efficient Matlab LMI toolbox, and no tuning of parameters is required. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.
Description: This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.
Sponsorship: This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany.
ISSN: 0893-6080
Appears in Collections:Computer Science
Dept of Computer Science Research Papers

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