iISS implies an iISS Lyapunov–Krasovskii functional with point-wise dissipation

Consider the time-delay system on $\mathcal X^n$ with inputs in $\mathcal U^m$. Converse point-wise iISS-LKF conjecture. If the system is iISS, then it admits an iISS Lyapunov–Krasovskii functional with point-wise dissipation. The survey establishes the forward implication from such a functional to iISS, while the converse remains unresolved; its resolution is not supplied.