Feedback realizations in linear multivariable systems

A feedback system consists of two objects, a fixed parent system and a controller connected to it. The relationship between external and internal descriptions of such systems is described. It is shown that redundancy in a feedback system can be expressed as a partial reduction with respect to controllability and observability. Applying this reduction yields a controller of lowest possible order. It is also shown that the requirement of internal stability can be expressed as a requirement on the external description of the feedback system only. This leads to a nice formalism for internally stable control synthesis using rational matrices. This is demonstrated in two important control problems, the model matching problem and the algebraic regulator problem, and by examples.