Exponential stability in Lagrange sense for inertial neural networks with time-varying delays

Abstract

This paper addresses the global exponential stability in Lagrange sense for inertial neural networks (INNs) with time-varying discrete delays and distributed delays. By utilizing a proper variable substitution to transform the original system into a first-order differential system, choosing an appropriate Lyapunov–Krasovskii functional (LKF), applying Jensen inequality, Jensen-based inequality, Wirtinger-based integral inequality and improved reciprocally convex inequality to estimate the derivative of the LKF, several sufficient conditions, which guarantee the global exponential stability in Lagrange sense for the INNs, are newly obtained in terms of linear matrix inequalities. Meanwhile, the detailed estimation for global exponential attractive set is also given. And two numerical examples are provided to validate the effectiveness of the proposed results.