The problem of robust matrix root-clustering against additive structured uncertainty is addressed. A bound on the size of the uncertainty domain preserving matrix D-stability is derived from an LMI approach. A recently proposed sufficient condition for robust matrix D-stability with respect to convex polytopic uncertainty is used. It is relevant to the framework dealing with parameter-dependent Lyapunov functions. Using this condition, the problem of computing the robustness bound is formulated as a generalised eigenvalue problem, that enables the bound value to be maximised.