Stability and synchronization control of inertial neural networks with mixed delays

Abstract

This paper analyzes the stability and synchronization control of inertial neural networks (INNs) with both time-varying delay and coupling delay by transforming them into the first-order systems. We show that there exists a unique equilibrium point (EP) by generalized nonlinear measure (GNM) approach, and provide a criterion to ensure the global asymptotic stability (GAS) of the EP by defining an appropriate Lyapunov–Krasovskii functional (LKF). Moreover, for the addressed systems under parameter mismatch, the quasi-synchronization is realized by applying the generalized Halanary inequality and matrix measure (MM), and an adaptive controller is designed to achieve the global asymptotic synchronization. The obtained results improve some exiting ones and are easy to be checked. Finally, the validity of the obtained results is supported by some numerical examples.