Complete Synchronization of Discrete-Time Fractional-Order T-S Fuzzy Complex-Valued Neural Networks With Time Delays and Uncertainties

This article aims to probe synchronization problem of discrete-time fractional-order T-S fuzzy complex-valued neural networks (DFTSFCNNs) with time delays and uncertainties. First, three important power-law inequalities regarding Caputo fractional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\theta$</tex-math></inline-formula>-difference are strictly attested. Next, a fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$m$</tex-math></inline-formula>-norm Lyapunov function (FMLF) that relies on membership functions is designed to replace traditional Lyapunov functions and obtain synchronization criteria. Then, a unique complex-valued fuzzy nonlinear delayed feedback controller is devised, and by virtue of the FMLF method and newly derived inequalities herein, several sufficient criteria are derived to ensure complete synchronization of DFTSFCNNs. Lastly, the validity of the main results is demonstrated by numerical simulations, and an application of the obtained results in image encryption is also provided.