New results for the stability of fractional-order discrete-time neural networks

Fractional-order discrete-time neural networks represent a class of discrete systems described by non-integer order difference operators. Even though the stability of these networks is a prerequisite for their successful applications, very few papers have been published on this topic. This paper aims to make a contribution to these stability issues by presenting a network model based on the nabla Caputo h-discrete operator and by proving its Mittag-Leffler stability. Additionally, a class of variable fractional-order discrete-time neural network is introduced and a novel theorem is proved to assure its asymptotic stability. Finally, simulation results are carried out to highlight the effectiveness of the stability approach illustrated herein.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).