On relations between Schmidt pairs arising in robust control

We present here some generalizations and some simpler derivations of results appeared in Fuhrmann [4] and Fuhrmann and Ober [5]. The main result is that the singular values and Schmidt vectors of the Hankel operator with symbol a normalized coprime factorization of a plant can be given an explicit representation in terms of the plant, of its optimally robust controller and of the Schmidt pairs of another scalar Hankel operator. This enables a simple connection between the original plant and what is called ”caracteristic function” 1991 Mathematics Subject Classification: 93B36, 93B28