Robust stability analysis in the *-norm and Lyapunov-Razumikhin functions for the stability analysis of time-delay systems

Lyapunov-Krasovskii functionals have been shown to have connections with input-output techniques considering delay operators mapping L
₂
to L
₂
. It is shown here that Lyapunov-Razumikhin functions can also be connected to the input-output framework by considering operators on L
_∞
and the corresponding Small-Gain Theorem. Several important results from the Lyapunov-Razumikhin Theorem are retrieved and extended.