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A robust matrix root-clustering analysis for descriptor systems is considered. It states a necessary and sufficient condition for a descriptor system to be regular, impulse free and to have its finite poles in a specified region of the complex plane. This region is a union of convex and possibly disjoint and non-symmetric subregions. A sufficient condition to preserve those properties in the presence of polytopic and norm-bounded uncertainties affecting the state matrix is also established. This condition is based upon the implicit derivation of parameter-dependent Lyapunov functions. All the conditions are expressed in terms of linear matrix inequalities.