ISS Lyapunov-Krasovskii theorem with point-wise dissipation: a V-stability approach

We show that the existence of a Lyapunov-Krasovskii functional (LKF) with a point-wise dissipation suffices for ISS of time-delay systems, provided that uniform global stability can also be ensured using the same LKF. To prove this result, we develop a stability theory, in which the behavior of solutions is not assessed through the classical norm but rather through a specific LKF, which may provide significantly tighter estimates.