Degenerating families of linear dynamical systems I

This paper addresses itself to the question whether Mm,n,p cr,co(IR), the space of equivalence classes of completely reachable and observable linear dynamical systems under state space equivalence, can be compactified in a system theoretically meaningful way by adding e.g. lower dimensional systems. We obtain a partial compactification Mm,n,p -(IR) by adding lower dimensional systems, differential operators and mixtures of these two. This partial compactification is wellbehaved with respect to the limiting input-output behaviour of (degenerating) families of linear dynamical systems. The compactification is also maximal in the sense that if the input-output behaviours of a family of systems (Fz, Gz, Hz) have a (noninfinite) limit than that limit is the input-output behaviour of one of the points of Mm,n,p -(IR).