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

Abstract

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.

Keywords

• Neural networks
• Nabla Caputo h-discrete operator
• Discrete Laplace transform method
• Banach contraction mapping
• Mittag–Leffler stability
• Variable fractional-order discrete-time neural networks