Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions

It is demonstrated that many previously reported Lyapunov-based stability conditions for time-delay systems are equivalent to the robust stability analysis of an uncertain comparison system free of delays via the use of the scaled small-gain lemma with constant scales. The novelty of this note stems from the fact that it unifies several existing stability results under the same framework. In addition, it offers insights on how new, less conservative results can be developed.