Globally exponential stability of a certain neutral differential equation with time-varying delays

Abstract

In this paper, an improved globally exponential stability criterion of a certain neutral delayed differential equation with time-varying of the form d dt [x(t) + px(t - τ (t))] = -ax(t) + b tanh x(t - Σ (t)) has been proposed in the form of linear matrix inequality. We first propose an upper bound of the solution in terms of an exponential function. Then we apply Lyapunov functions, a descriptor form, the Leibniz-Newton formula and radially unboundedness to formulate the sufficient criterion. To show the effectiveness of the proposed criterion, four numerical examples are presented. © 2014 Keadnarmol and Rojsiraphisal; licensee Springer.