TY  - RPRT
A1  - Zerz, Eva
T1  - Algebraic Systems Theory
N2  - 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).
T3  - Berichte der Arbeitsgruppe Technomathematik (AGTM Report) - 259 
KW  - Abstract linear systems theory
KW  - basic systems theoretic properties
KW  - One-dimensional systems
KW  - Multi-dimensional systems
Y1  - 2004
UR  - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1567
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-15679
N1  - Altdaten, kein Volltext verfügbar ; Printversion in Bereichsbibliothek Mathematik vorhanden: MAT 144/620-259
ER  -