On Synchronization of Coupled Delayed Neural Networks

In this chapter, the global synchronization problem is investigated for both continuous- and discrete-time coupled neural networks. The neural networks appear in the form of coupled arrays, where both the linear and nonlinear couplings are taken into account. The activation functions include both the Lipchitz-type and the sector-type ones. Due to the high dimension of the system under consideration, the Kronecker product is utilized to facilitate the derivation and simplify the presentation. By resorting to the matrix functional method, we aim to establish sufficient conditions under which the considered array of neural networks is globally synchronized. It is shown that the globally exponential synchronization can be achieved by suitably designing the coupling matrix, the inner linking matrix and some free matrices representing the relationships between the system matrices. The sufficient conditions obtained that guarantee the synchronization are directly related to several matrix quantities describing the coupling topology. Furthermore, these conditions are expressed in terms of several linear matrix inequalities (LMIs) which can be easily verified by utilizing the numerically efficient Matlab LMI toolbox. Several illustrative examples are given to show the feasibility and applicability of the proposed synchronization scheme.

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