In this paper, under the assumption that all the eigenvalues of a linear nominal discrete time-delay system lie within a specified ring region, a sufficient condition is proposed to preserve the assumed property when the structured parameter perturbations are added into the linear nominal discrete time-delay system. For the case of eigenvalue-clustering in a circular region, and for the case of not including time delays, the presented sufficient condition is mathematically proved to be less conservative than those reported recently in the literature.