Complete synchronization for discrete-time fractional-order coupled neural networks with time delays

This paper is devoted to investigating complete synchronization for a class of discrete-time fractional-order coupled neural networks (DFCNNs) with time delays, which has not been documented yet. For the sake of answering the challenging problem mentioned above, we generalize the classic Barbalat’s lemma to discrete-time fractional-order (DF) version. After that a novel hybrid controller composed of adaptive control term and delayed feedback control term is firstly designed to reach synchronization of DFCNNs with time delays. Then, several well-done synchronization criteria are acquired by the utilization of fractional calculus theory, DF Barbalat’s lemma and inequality techniques. In the end, a numerical example is put forward to exemplify the validity of our results.