Further results on stability and synchronization of fractional-order Hopfield neural networks

This paper focuses on stability and synchronization of fractional-order Hopfield neural networks. By taking information on activation functions into account, two novel convex Lyapunov functions are constructed: one is a fractional-order-dependent Lyapunov function, and the other is a new quadratic Lyapunov function. Based on these two Lyapunov functions, together with a fractional-order differential inequality, a fractional-order-dependent Mittag-Leffler stability criterion is derived for fractional-order Hopfield neural networks, which is in the form of linear matrix inequalities (LMIs). Moreover, a Mittag-Leffler synchronization criterion in terms of LMIs is presented for drive-response fractional-order Hopfield neural networks under linear control. Finally, three numerical examples are provided to indicate the benefits and less conservatism of the obtained criteria in this paper. (C) 2019 Elsevier B.V. All rights reserved.