Globally exponential stability of a certain neutral differential equation with time-varying delays
Panuwat Keadnarmol, Thaned Rojsiraphisal · Advances in Difference Equations · 2014
In this paper, an improved globally exponential stability criterion of a certain neutral delayed differential equation with time-varying of the form d d t [ x ( t ) + p x ( t − τ ( t ) ) ] = − a x ( 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.