A new approach is presented to obtain a convex set of robust D—stabilizing fixed structure controllers, relying on Cauchy's argument principle. A convex set of D—stabilizing controllers around an initial D—stabilizing controller for a multi-model set is represented by an infinite set of Linear Matrix Inequalities (LMIs). By appropriate sampling of the D—stability boundary, a Semi-Definite Programming (SDP) is proposed that can be integrated in other synthesis approaches to ensure D—stability along other design specifications. To showcase utility of the proposed approach, two different examples are given: a boost converter with multi-model uncertainty and a laser-beam system modeled by an identified finite impulse response.