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Vietnam Journal of Mathematics 40:1 (2012) 79-93

New Criteria for Stability and Stabilization of

Neural Networks with Mixed Interval Time-Varying Delays

Mai Viet Thuan¹ and Vu Ngoc Phat²

¹Department of Mathematics, Thai Nguyen University, Thai Nguyen, Vietnam

²Institute of Mathematics, VAST, 18 Hoang Quoc Viet, Hanoi, Vietnam

Received July 15, 2011

Revised August 26, 2011

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.

2000 Mathematics Subject Classification. 34D20, 37C75, 93D20.

Keywords. Neural networks, stability, stabilization, non-differentiable delays, Lyapunov function, linear matrix inequalities.

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Published by Springer since January 2013