Mittag–Leffler stability and synchronization of neutral-type fractional-order neural networks with leakage delay and mixed delays

Abstract

In recent years, there have been a lot of studies focusing on the dynamics of fractional-order neural networks (FONNs). One problem is that the standard Lyapunov theory does not apply to fractional-order systems, so these studies rely on the use of Halanay-type lemmas to develop sufficient criteria for certain dynamic properties of FONNs, which frequently results in much more conservative criteria than the ones obtained for integer-order neural networks. The present research uses the Halanay-type lemma in a novel way, in order to obtain less conservative sufficient criteria than previous studies. On the other hand, the previous research only considers FONNs with some types of delays, thus limiting their applicability in real-life scenarios, where possibly many more types of delays are relevant. To address this issue, the paper discusses very general FONNs that include neutral-type delay, leakage delay, time-varying delays, and distributed delay. This is the first time such a general model for the fractional-order scenario has been developed, to our awareness. Three theorems, each based on a distinct Lyapunov-like function, are used to construct sufficient criteria, given in terms of linear matrix inequalities, which ensure, respectively, the Mittag–Leffler stability and synchronization, using two different and general state feedback control schemes, of the proposed networks. The usage of the free weighting matrix approach, among the first times in the context of FONNs, also significantly contributes to reducing the conservatism of the deduced sufficient conditions. One numerical example is provided to illustrate each of the three theorems.