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

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