Robust synchronisation of delayed neural networks with both linear and non-linear couplings

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In this article, the globally robust synchronisation problem is investigated for an array of coupled neural networks with uncertain parameters and time delays. Both the cases of linear coupling and non-linear coupling are simultaneously taken into account. By resorting to the Kronecker product properties, matrix functional method and matrix inequality techniques are exploited to establish sufficient conditions under which the considered uncertain neural networks are globally robustly synchronised. It is shown that robust exponential synchronisation of the coupled neural networks is guaranteed by a suitable design of the coupling matrix, the inner linking matrix and some free matrices representing the relationships between the system matrices. The conditions obtained are related to several matrix quantities describing the coupling topology. They are expressed in terms of several linear matrix inequalities which can therefore be easily verified by utilising the numerically efficient Matlab LMI toolbox. A commonly used example with chaotic nodes is given to illustrate the effectiveness of the proposed synchronisation scheme.