  For time-delay systems, it is known that global asymptotic stability is
guaranteed by the existence of a Lyapunov-Krasovskii functional that dissipates
in a point-wise manner along solutions, namely whose dissipation rate involves
only the current value of the solution's norm. So far, the extension of this
result to global exponential stability (GES) holds only for systems ruled by a
globally Lipschitz vector field and remains largely open for the input-to-state
stability (ISS) property. In this paper, we rely on the notion of exponential
ISS to extend the class of systems for which GES or ISS can be concluded from a
point-wise dissipation. Our results in turn show that these properties still
hold in the presence of a sufficiently small additional term involving the
whole state history norm. We provide explicit estimates of the tolerable
magnitude of this extra term and show through an example how it can be used to
assess robustness with respect to modeling uncertainties.

Optimization and Control