Fuzzy-Model-Based $\mathcal {H}_{\infty }$ Pinning Synchronization for Coupled Neural Networks Subject to Reaction–Diffusion

Abstract

This article investigates the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> synchronization problem for fuzzy coupled neural networks subject to reaction–diffusion. An available control method, namely, the adaptive pinning control strategy, is employed. In view of such a method, one may accomplish control objectives by controlling a small number of nodes instead of all nodes, and in this regard, it is possible to reduce the control cost to some extent, and the method can adaptively adjust the coupling strength as well. Furthermore, a novel inequality is introduced, which can ensure that the developed results are less conservative compared with some existing ones of dealing with the reaction–diffusion terms. Then, through the utilization of fuzzy set theory together with Lyapunov stability theory, some sufficient conditions with the ability to ensure the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance level of the resulting synchronization error system are deduced. Finally, an illustrative example is presented to show the advantages and effectiveness of the proposed methods.