Global exponential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si491.svg" display="inline" id="d1e399"> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:math> synchr

This paper investigates the global exponential H ∞ synchronization problem for multi-weighted coupled neural networks (MWCNNs) with multiple time-varying delays. A bounded real lemma (BRL) is firstly established based on the solutions of delayed MWCNNs, which can be used to derive that delayed MWCNNs reach global exponential H ∞ synchronization. On the basis of the proposed BRL, an aperiodically intermittent controller (AIC) for delayed MWCNNs is proposed to improve synchronization performance. As no Lyapunov–Krasovskii functional (LKF) is constructed in the proposed method, the computational complexity is significantly reduced. Finally, the theoretical result is verified through a numerical example, and applied to encryption and decryption of color images. • The solutions of the considered system is first given. • A BRL is given based on the obtained solutions to achieve synchronization. • To improve the synchronization property, an AIC is designed based on the derived BRL. • Limits on time-varying delay’s derivative is lifted. LKFs do not need to be constructed.