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Vietnam Journal of Mathematics 40:1 (2012)
79-93
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New Criteria for Stability and Stabilization of
Neural Networks with Mixed Interval Time-Varying
Delays
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Mai Viet Thuan1 and Vu Ngoc
Phat2
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1Department of Mathematics, Thai Nguyen
University, Thai Nguyen, Vietnam
2Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam
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Received July 15, 2011
Revised August 26, 2011
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Abstract. This paper considers the global
exponential stability and stabilization for a class of neural networks with
mixed interval time-varying delays. The time delay is assumed to be a
continuous function belonging to a given interval, but not necessary to be
differentiable. By constructing a set of new Lyapunov-Krasovskii
functionals combined with Newton-Leibniz formula,
new delay-dependent criteria for exponential stability and stabilization of
the system are established in terms of linear matrix inequalities
(LMIs), which allows to compute simultaneously the two bounds that
characterize the exponential stability of the solution. Numerical examples
are included to illustrate the effectiveness of the results.
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2000 Mathematics
Subject Classification. 34D20, 37C75, 93D20.
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Keywords.
Neural networks, stability, stabilization, non-differentiable delays, Lyapunov function, linear matrix inequalities.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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