Neutral-type, leakage, and mixed delays in fractional-order neural networks: asymptotic synchronization analysis

The dynamics of fractional-order neural networks (FONNs) are challenging to study, since the traditional Lyapunov theory does not apply to them. Instead, Halanay-type lemmas are used to create sufficient criteria for specific dynamic properties of FONNs. The application of these lemmas, however, typically leads to conservative criteria. The Halanay-type lemma is used in a novel way in this study to develop less conservative sufficient conditions in terms of linear matrix inequalities (LMIs) for extremely general FONNs, with different types of delays, such as neutral-type, leakage, time-varying, and distributed delays. The formulation of such a general model for the fractional-order scenario is done here for the first time. In addition, a new Lyapunov-like function is established, resulting in algebraic conditions that are less conservative. Three theorems are put forward that build sufficient criteria for the asymptotic synchronization, employing state feedback control, of the proposed networks, each based on a different Lyapunov-like function. For the first time in the context of FONNs, the free weighting matrix technique is also used to greatly decrease the conservatism of the obtained sufficient conditions. One numerical simulation illustrates each of the three theorems.