This paper is concerned with the characterization of the Hurwitz stability of matrices, which can be written as the product of two square matrices AD with A precisely known and D belonging to the set of all positive diagonal matrices, and the Schur stability of matrices AD for all diagonal D, whose entries have absolute magnitude less than or equal to 1, known as the problem of D-stability. Sufficient conditions are given in terms of linear matrix inequalities formulated at the vertices of an adequately chosen polytope domain, allowing simple and numerically efficient evaluations of D-stability. The conditions proposed provide less conservative results and encompass previous conditions from the literature, as illustrated by examples.262415425