Simultaneous stabilization of linear systems under stable additive or feedback perturbations

In the standard linear, time-invariant, multi-input multi-output unity-feedback system, it is shown that a given plant and one obtained by a known stable additive (or feedback) perturbation of this plant can be simultaneously stabilized by a common controller. The plant is not necessarily stable. No small-gain restrictions are imposed on the stable perturbations. A set of simultaneously stabilizing controllers is explicitly derived for any such pairs of plants. The results extend the standard single connected set of plants description in robust control design methods to two (possibly disjoint) sets of plants.