Interval matrix method based synchronization criteria for fractional-order memristive neural networks with multiple time-varying delays

This paper addresses the issue of globally asymptotical synchronization of fractional-order memristive neural networks (FMNNs) with multiple time-varying delays. First, a more practical model for FMNNs with multiple time-varying delays is proposed because of considering the characteristics of a real memristor. Under the framework of differential inclusions, the FMNN is transformed into a fractional-order neural network (FNN) with interval uncertainties. Thus, the synchronization of two FMNNs is converted into the synchronization of two FNNs with interval parameters. The main problems to overcome are: (1) establishing an effective differential inequality for fractional-order systems with multiple time-varying delays; (2) finding a better upper bound for the norm of interval matrices. In this paper, a new upper bound for the norm of interval matrices is derived and meanwhile the fractional Halanay inequality is generalized to the case of multiple time-varying delays. Then, synchronization control strategies are elaborately designed to achieve globally asymptotical synchronization. By exploiting the newly-built fractional Halanay inequality and constructing appropriate Lyapunov functions, some new sufficient conditions for globally asymptotical synchronization of FMNNs with time-varying delays are derived. The synchronization criteria, expressed by LMIs, are easy to check and extend some previously published results. An illustrative numerical example is given to demonstrate the effectiveness of the theoretical results. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.