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

TL;DR

This paper establishes necessary and sufficient conditions for stability of neutral functional differential equations using Lyapunov-Krasovskii functionals, linking stability concepts and providing theoretical insights.

Contribution

It introduces Lyapunov-Krasovskii theorems for neutral systems in Hale's form, extending stability analysis with new necessary and sufficient conditions.

Findings

Lyapunov-Krasovskii functional existence characterizes stability

Conditions for uniform global asymptotic and exponential stability

Connection between exponential stability and input-to-state stability

Abstract

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.