Characterization of controllers in simultaneous stabilization

This paper gives a convenient parametrization for the class of all stabilizing controllers for two or more plants. The result represent a generalization of the Youla parametrization of the class of all stabilizing controllers in terms of an arbitrary stable proper transfer function. Although, as expected, the additional constraints for simultaneous stabilization are not readily incorporated into H∞, H2 optimization procedures as in the standard case, there is immediate application of the theory for reduction of controllers which simultaneously stabilize two or more plants.