In this note, we consider the structural stability of an unstable plant, feedback stabilized by a controller. It is shown that infinitesimal parameter perturbations in the plant transfer matrix can destabilize the stable feedback control system obtained from a minimal realization of the ¿nominal plant.¿ The remedy for such structural instability consists in using a minimal realization in which the dimension of the ¿antistable part¿ is maximized over the uncertain parameter values. This requires knowledge of the ¿correct class¿ of parametrizations to which the nominal plant transfer matrix belongs.