A partial compactification for linear systems (Q1091991)

For the space Rat(n) of all proper rational transfer functions g(s)\(\in R(s)\) with McMillan degree n, the closure problem for Rat(n) in the affine space E of finite \(N\times N\) Hankel matrices (n\(\leq N-1)\) is studied. The main result of the paper consists in proving that the closure \(\overline{Hank(n,N)}\) of Rat(n) in E is given by all Hankel matrices of rank less than or equal to n. This partial compactification differs from a corresponding result delivered by Deistler and Hannan because there exist boundary points which cannot be interpreted as linear systems of order \(<n.\) The last section of the paper deals with a related closure problem for partial realizations.