In this paper, the problem of robust matrix root-clustering is addressed. An LMI approach is used to derive a sufficient condition for robust D-stability with respect to convex polytopic uncertainty. The presented results are part of the new framework dealing with parameter-dependent Lyapunov functions. The main contribution is to propose a new condition for matrix D-stability where D is a union of possibly disjoint and nonsymmetric subregions of the complex plane. A numerical comparison is proposed between this condition and a more classical one based on quadratic stability.