Virginia Polytechnic Institute and State University
Zero-pole interpolation of nonregular rational matrix functions
Abstract
dc:description.abstractIn this thesis the right and left pole structure of a not necessarily regular rational matrix function W is described in terms of pairs of matrices-right and left pole pairs. The concept of orthogonality in R<sup>n</sup> is investigated. Using this concept, the right and left zero structure of a rational matrix function W is described in terms of pairs and triples of matrices-right and left null pairs and right and left kernel triples. The definition of a spectral triple of a regular rational matrix function over a subset σ of C is extended to the nonregular case. Given a rational matrix function W and a subset σ of C, the left null-pole subspace of W over σ is described in terms of a left kernel triple and a left σ-spectral triple for W. A sufficient condition for the minimality of McMillan degree of a rational matrix function H which is right equivalent to W on σ, that is a rational matrix function H of the same size and with the same left null-pole subspace over σ as W, is developed. An algorithm for constructing a rational matrix function W with a left kernel triple (A<sub>κ</sub> B<sub>κ</sub> D<sub>κ</sub>) and left null and right pole pairs over σ⊂C (A<sub>ζ</sub>, B<sub>ζ</sub>) and (C<sub>π</sub>, A<sub>π</sub>), respectively, from a regular rational matrix function with left null and right pole pairs over σ (A<sub>ζ</sub>, B<sub>ζ</sub>) and (C<sub>π</sub>, A<sub>π</sub>) is described. Finally, a necessary and sufficient condition for existence of a rational matrix function W with a given left kernel triple and a given left spectral triple over a subset σ of C is established.
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Polytechnic Institute and State University
- Year dc:date.issued
- 1989
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Rakowski, Marek
- Chair dc:contributor.committeechair
-
- Ball, Joseph A.
- Committee members dc:contributor.committeemember
-
- Hannsgen, Kenneth B.
- Thomson, James E.
- Wheeler, Robert
- Brown, Ezra A.
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en_US
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- http://hdl.handle.net/10919/54268
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/54268