This paper considers the problem of robust stability for linear systems with a constant time-delay in the state and subject to real convex polytopic uncertainty. First of all, for robust stability problem, we exploit new matrix inequalities characterization of delay-dependent robust stability results, and demonstrate that it allows the use of parameter-dependent Lyapunov functions in comparison to the classical one, whose drawback stands in the use of a single Lyapunov function to assess the stability over the whole uncertainty domain. Next, as for delay dependent case, the problem of determining the maximum time-delay under which the system will remain stable is cast into a generalized eigenvalue problem and thus solved by LMI techniques. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.