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

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

AMS Subject Classifications: :

• 37Fxx
• 34D20
• 34D23
• 82C32
• 37N35

Acknowledgements

This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, an International Joint Project sponsored by the Royal Society of the UK and the NSFC of China, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, the National Natural Science Foundation of China under Grants 60774073, 10471119 and 10671172, and the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002.