Asymptotic synchronization for the inertial neural networks by using the differential inequality skills

Abstract

This paper explores the asymptotic synchronization (AS) for a class of master-slave inertial neural networks (MSINNs). Without employing the existing study approaches such as matrix measure means (MMMs) and linear matrix inequality (LMI), by planning two classes of novel controllers of the trigonometric functions, two criteria to assure the AS for the considered MSINNs are achieved by utilizing the implicit zero point existence theorem of functions and differential inequality way (DIW). By applying the implicit point existence theorem of functions and constructing the controllers of the trigonometric functions, the more concise and more easily verified results on AS can be obtained for neural networks (NNs) than using LMI and MMMs. Our results reveal that the time delay plays a important part in the AS of the considered networks. Namely, when the time delay is less than a certain constant, the AS between the master system and the slave system can be achieved.