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Synchronisation of chaotic delayed artificial neural networks: an ℍ ∞ control approach

This article presents a new linear matrix inequality-based approach to an ℋ∞ output feedback control problem of master—slave synchronisation of artificial neural networks with uncertain time-delay, which can exhibit chaotic behaviour. The uncertain time-delay is considered as a composition of a nominal positive value subject to a time-varying perturbation. The methodology to be employed is based on the selection of a new discretised Lyapunov–Krasovskii functional (LKF) with two parts: the first is related to the nominal delay, and the second one is related to the time-varying perturbation. Extra manipulations allows us to introduce free matrices decoupling the LKF matrices from the system matrices, turning to obtain a control design condition easier. Finally, an insightful numeric simulation will be proposed to show the effectiveness of this kind of methodology to the problem of synchronising coupled chaotic delayed artificial neural networks. Besides, based on the information transmission via control principle, two information transmission experiments are performed as a possible application or/and an index to measure the effectiveness of the proposed approach.