Stabilization and control design by partial output feedback

We consider a (not necessarily proper) plant input/output behavior which shall be stabilized by a proper controller via partial output feedback such that also the feedback behavior is a proper input/output behavior. In addition a control task like tracking or disturbance rejection shall be performed. The setting includes both the continuous and the discrete time case, and stability is defined with respect to a set T of stable polynomials. The standard choice for T yields asymptotic stability. Our approach relies on the fact that the signal module is an injective cogenerator over the ring of operators and this property is preserved under localization with respect to the set T. We present a condition ensuring the existence of proper compensators such that the feedback behavior is proper and stable and such that the given control task is performed. If this condition is satisfied we construct a large class of such compensators.