A note on computing range space bases of rational matrices
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2017
- DOI:
- 10.48550/arXiv.1707.00489
- arXiv:
- arXiv:1707.00489
- Bibcode:
- 2017arXiv170700489V
- Keywords:
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- Computer Science - Systems and Control;
- 26C15;
- 93B40;
- 93C05;
- 93B55;
- 93D15
- E-Print:
- 8 pages