Algebraic Systems Theory

  • Control systems are usually described by differential equations, but their properties of interest are most naturally expressed in terms of the system trajectories, i.e., the set of all solutions to the equations. This is the central idea behind the so-called "behavioral approach" to systems and control theory. On the other hand, the manipulation of linear systems of differential equations can be formalized using algebra, more precisely, module theory and homological methods ("algebraic analysis"). The relationship between modules and systems is very rich, in fact, it is a categorical duality in many cases of practical interest. This leads to algebraic characterizations of structural systems properties such as autonomy, controllability, and observability. The aim of these lecture notes is to investigate this module-system correspondence. Particular emphasis is put on the application areas of one-dimensional rational systems (linear ODE with rational coefficients), and multi-dimensional constant systems (linear PDE with constant coefficients).

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Metadaten
Author:Eva Zerz
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15679
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (259)
Document Type:Report
Language of publication:English
Year of Completion:2004
Year of Publication:2004
Publishing Institute:Technische Universität Kaiserslautern
Tag:Abstract linear systems theory ; Multi-dimensional systems; One-dimensional systems ; basic systems theoretic properties
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik

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