On stability and event trigger control of fractional neural networks by fractional non-autonomous Halanay inequalities

This paper studies the stability and control of fractional neural networks by Halanay inequality technique. Based on the fractional comparison principle and supremum and infimum principle, a novel fractional non -autonomous Halanay inequality is developed. The fractional non-autonomous Halanay inequality is in a form of integral, which considers the global nature of the system parameters and reduces estimation error. By combining the Halanay inequality with a maximum auxiliary function, an asymptotically stable discriminant condition for fractional Hopfield time-delay neural networks is established in an algebraic form. Moreover, event trigger control for fractional neural networks is studied. Low network bandwidth costs and high control efficiency are guaranteed by a Mittag-Leffler type event-triggered mechanism. Then, a discriminant condition on the event trigger control for fractional neural networks is established. The advantages of the proposed methods are demonstrated by three numerical examples.