Regulator synthesis using (C, A, B)-pairs

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Abstract
The concept of a (C, A, B)-pair of subspaces was introduced in an earlier paper by the author to study problems of compensator design. Here, it is shown that the same concept plays a basic role in the theory of tracking and regulation. From a few fundamental properties, the main results of regulator theory are derived in a relatively simple and straightforward manner. Another new feature is that we are able to allow the presence of an unknown input, thereby unifying the fields of "tracking and regulation" and "disturbance decoupling." All results are fully constructive, and an example is given to illustrate the theory.