A new robust delay dependent stability test is introduced that determines the asymptotic stability of linear systems with state delays. The parameters of the system are not exactly given. They are known to reside in a given polytope. The test provides an efficient sufficient condition for the stability of the system over the uncertainty polytope. This condition is parameter dependent and it therefore improves previous results that were derived using a single Lyapunov-Krasovskii functional. The stability test is readily extended to provide a criterion for robust stabilization via state-feedback.