Lyapunov-Krasovskii characterization of the input-to-state stability for neutral systems in Hale's form

The primary contribution of the paper is to show that the Lyapunov-Krasovskii conditions available in the literature, for checking the input-to-state stability property of systems described by neutral functional differential equations in Hale's form, are also necessary. It is shown that the Lyapunov-Krasovskii conditions available in the literature are equivalent to the input-to-state stability property, for an enlarged class of neutral systems. Finally, a novel necessary and sufficient condition for the input-to-state stability property is provided.