In 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. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/54268 |
| Date | January 1989 |
| Creators | Rakowski, Marek |
| Contributors | Mathematics, Ball, Joseph A., Hannsgen, Kenneth B., Thomson, James E., Wheeler, Robert, Brown, Ezra A. |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | vi, 107 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 21274104 |
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