A note on computing range space bases of rational matrices
For researchers in systems and control theory, this provides a unified computational method for range space bases, but it is incremental as it extends existing Kronecker-like form techniques.
This paper presents computational procedures based on descriptor state-space realizations to compute proper range space bases of rational matrices, enabling extraction of full column rank factors. The approach accommodates various basis types and has applications in factorizations and pseudo-inverses.
We discuss computational procedures based on descriptor state-space realizations to compute proper range space bases of rational matrices. The main computation is the orthogonal reduction of the system matrix pencil to a special Kronecker-like form, which allows to extract a full column rank factor, whose columns form a proper rational basis of the range space. The computation of several types of bases can be easily accommodated, such as minimum-degree bases, stable inner minimum-degree bases, etc. Several straightforward applications of the range space basis computation are discussed, such as, the computation of full rank factorizations, normalized coprime factorizations, pseudo-inverses, and inner-outer factorizations.