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

Abstract 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.