Discrete-Time Fractional-Order T-S Fuzzy Neural Networks With Uncertain Parameters: Synchronization and Image Encryption

This article explores complete synchronization (CS) of discrete-time fractional-order T-S fuzzy neural networks (NNs) with mixed delays and uncertain parameters. First, a flexible weighted 2-norm inequality on the nabla $\omega $ -order Caputo $\varsigma $ -difference operator is established, providing a new theoretical framework for synchronization analysis of discrete-time fractional-order dynamical systems. Next, a hybrid control strategy is proposed, demonstrating strong robustness against system uncertainties. By leveraging our proposed inequality and associated analytical techniques, some easily verifiable CS criteria are presented in the form of linear matrix inequalities. Finally, numerical simulations are presented to validate the theoretical results and illustrate their effective application in image encryption.