Quasi-Projective Synchronization of Discrete-Time Fractional-Order T-S Fuzzy Complex-Valued Neural Networks With Hybrid Delays

This article delves into quasi-projective synchronization (Q-PS) problem for a class of discrete-time fractional-order T-S fuzzy complex-valued neural networks (DFTSFCNNs) with leakage and time-varying delays. First of all, according to the theory of discrete fractional calculus and properties of Mittag-Leffler function, an innovative property of discrete Mittag-Leffler function is strictly proved, and then an inequality for dealing with mixed time delays is rigorously derived. Next, by utilizing Caputo fractional difference theory and combining with property and the inequality offered in this article, some easily verifiable Q-PS criteria are derived under complex-valued fuzzy linear controller. Eventually, a numerical example is presented to demonstrate availability of the derived results. Note to Practitioners—Leakage delay and time-varying delay are core factors influencing the dynamic behavior of complex systems, as they directly impact synchronization control, controllability, and stability. Ignoring them may lead to model distortion or control failure. Therefore, this paper proposes a new inequality for handling mixed delays in the quasi-projective synchronization of DFTSFCNNs with leakage delay and time-varying delay. Based on this inequality, delay-dependent criteria for the quasi-projective synchronization are established, which breaks the traditional limitation of using delayed controllers to handle time-delay terms. In addition, numerical examples are used to verify the effectiveness of the quasi-projective synchronization criteria.