On a parameterization of all stabilizing controllers for plants with parametric uncertainty

A parametrization of all (internally) stabilizing controllers for SISO plants characterized by parametric uncertainty is obtained. The case of a single uncertain parameter is analyzed, and necessary and sufficient conditions for robust stability are derived. The results suggest the possibility of using this approach for synthesis of controllers for uncertain plants. The conditions in the multiparameter uncertainty case require more advanced tools for stability verification. A simple illustrative example is provided