Converse Lyapunov-Krasovskii Theorems for Systems Described by Neutral Functional Differential Equation in Hale's Form

In this paper we show that the existence of a Lyapunov-Krasovskii functional is necessary and sufficient condition for the uniform global asymptotic stability and the global exponential stability of time-invariant systems described by neutral functional differential equations in Hale's form. It is assumed that the difference operator is linear and strongly stable, and that the map in the right-hand side of the equation is Lipschitz on bounded sets. A link between global exponential stability and input-to-state stability is also provided. @ The extended version of this paper has been submitted to the International Journal of Control, Taylor & Francis.