Exploring projective synchronization in discrete-time fractional-order fuzzy cellular neural networks with distributed delays

Abstract

The projective synchronization (PS) of discrete-time fractional-order fuzzy cellular neural networks (DFFCNNs) with distributed delays is investigated in this paper. First, based on the nabla fractional-order difference theory, a comparison principle suitable for fractional-order systems with variable coefficients and multiple time delays is established, and the sub-multiplicative law of the nabla Mittag-Leffler function is rigorously proved. Second, a discrete-time fractional-order Halanay inequality with arbitrary step size, variable coefficients, and multiple time-varying delays is introduced. Furthermore, leveraging the aforementioned inequality, a sufficient condition for the PS of DFFCNNs is derived. Finally, an example is presented to confirm the validity of the results.