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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 L2 to L2. 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.