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On exponential stability of bidirectional associative memory neural networks with time-varying delays

For bidirectional associate memory neural networks with time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the Lyapunov functional method and linear matrix inequality (LMI) technique. A novel criterion for the stability, which give information on the delay-dependent property, is derived. | ARTICLE IN PRESS Available online at www.sciencedirect.com ScienceDirect CHAOS SOLITONS FRACTALS ELSEVIER Chaos Solitons and Fractals xxx 2007 xxx-xxx www.elsevier.com locate chaos On exponential stability of bidirectional associative memory neural networks with time-varying delays Ju H. Park a S.M. Lee b O.M. Kwon c a Department of Electrical Engineering Yeungnam University 214-1 Dae-Dong Kyongsan 712-749 Republic of Korea b Platform Verification Division BcN Business Unit KT Co. Ltd. Daejeon Republic of Korea c School of Electrical and Computer Engineering Chungbuk National University Cheongju 361-763 Republic of Korea Accepted 19 April 2007 Abstract For bidirectional associate memory neural networks with time-varying delays the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the Lyapunov functional method and linear matrix inequality LMI technique. A novel criterion for the stability which give information on the delay-dependent property is derived. A numerical example is given to demonstrate the effectiveness of the obtained results. 2007 Elsevier Ltd. All rights reserved. 1. Introduction As an extension of the unidirectional autoassociator of Hopfield 1 Kosko 2 has proposed a series of neural networks related to bidirectional associative memory BAM . This class of networks has good application in the area of pattern recognition and artificial intelligence. Therefore the BAM neural networks has been one of the most interesting research topics and has attracted the attention of many researchers. For instance refer to Refs. 3-10 . Also time delay will inevitably occur in the communication and response of neurons owing to the unavoidable finite switching speed of amplifiers in the electronic implementation of analog neural networks so it is more in accordance with this fact to study the BAM neural networks with time delays. The existence of time delay is frequently a source of .