Mittag–Leffler stability and stabilization of delayed fractional-order memristive neural networks based on a new Razumikhin-type theorem.

The Mittag–Leffler stability and stabilization of delayed fractional-order memristive neural networks(DFMNNs) are investigated in this paper. First, two new fractional Halanay inequalities are established by solving two fractional-order non-autonomous differential inequalities. Next, by using the proposed fractional Halanay inequalities, a novel Razumikhin-type theorem for Mittag–Leffler stability of delayed fractional-order systems is presented, which is an extension of the so-called Razumikhin theorem for integer-order delayed differential systems. Applying the Razumikhin-type theorem to the DFMNNs, several Mittag–Leffler stability and stabilization criteria are obtained. Finally, the validity of the proposed results is shown by two numerical examples. [ABSTRACT FROM AUTHOR]