Time-varying linear systems

The main goal of this thesis is to examine linear dynamical systems, both in the continuous- and discrete-time case, with time-varying coefficients using module theory and homological methods and to generalize results, such as the realization problem and matrix fraction descriptions, from the time-invariant case to the time-varying case. After a short introduction to behavioral systems theory we briefly describe the mathematical background of the algebraic approach. We then study structural properties such as autonomy, controllability, and observability. A realization problem of time-varying systems specified by a transfer matrix is also addressed. It is shown that realizability is equivalent to properness and minimality is equivalent to both controllability and observability. The notions of coprimeness of a matrix fraction description and row-properness of a skew polynomial matrix are introduced and used to determine the size of a minimal realization. An algorithm to transfer a given skew polynomial matrix into row-proper form is given and it is used to compute one sided greatest common divisors and least common multiples.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2007

Author dc:creator

• Belayneh, Berhanu Bekele

Contributors dc:contributor

• Zerz, Eva

• info:eu-repo/classification/ddc/510
• lineare dynamisch Systeme
• Mathematik
• linear dynamical systems
• injective cogenerator
• matrix fraction descriptions

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-123984%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:62413