Summary: We survey the theory of Béoutians with a special emphasis on its relation to system theoretic problems. Some instances are the connections with realization theory in particular signature symmetric realizations, the Cauchy index, stability, and the characterization of output feedback invariants. We describe canonical forms and invariants for the action of static output feedback on scalar linear systems of McMillan degree n.
Previous results on this subject are obtained in a new and unified way, by making use of only a few elementary properties of Bézout matrices. As new results we obtain a minimal complete set of 2n-2 independent invariants, an explicit example of a continuous canonical form for the case of odd McMillan degree, and finally a canonical form which induces a cell decomposition of the quotient space for output feedback