In this note, the delay-independent stability of delay systems is studied. It is shown that the strong delay-independent stability is equivalent to the feasibility of certain linear matrix inequality (LMI), that is to the existence of a quadratic Lyapunov-Krasovskii functional, independent of the (nonnegative) value of the delay. This constitutes the analogue of some well-known properties of finite-dimensional systems. This result is then applied to study delay-independent stability of systems with polytopic uncertainties.