On synchronization of coupled neural networks with discrete and unbounded distributed delays

Authors: Liu, Yurong¹; Wang, Zidong²; Liu, Xiaohui²

Source: International Journal of Computer Mathematics, Volume 85, Number 8, August 2008 , pp. 1299-1313(15)

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Abstract:

In this paper, we deal with the synchronization problem for an array of linearly coupled neural networks with simultaneous presence of both the discrete and unbounded distributed time-delays. By utilizing a novel Lyapunov-Krasovskii functional and the Kronecker product, it is shown that the addressed synchronization problem is solvable if several linear matrix inequalities (LMIs) are feasible. Hence, different from the commonly used matrix norm theories (such as the M-matrix method), a unified LMI approach is developed to establish sufficient conditions for the coupled neural networks to be globally synchronized, where the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. It is also shown that the synchronization of coupled neural networks with bounded distributed delays is just a special case of our main results. A numerical example is provided to show the usefulness of the proposed global synchronization condition.

Keywords: synchronization; neural networks; discrete time-delay; distributed time-delay; linear matrix inequality

Document Type: Research article

DOI: http://dx.doi.org/10.1080/00207160701636436

Affiliations: 1: Department of Mathematics, Yangzhou University, Yangzhou, P. R. China 2: Department of Information Systems and Computing, Brunel University, Uxbridge, Middlesex

Publication date: 2008-08-01

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