On Discrete Linear Systems
(2019) In Bachelor's Theses in Mathematical Sciences NUMK01 20181Mathematics (Faculty of Sciences)
- Abstract
- Linear time-invariant systems are ordinary differential equation systems that arise in control engineering where they are used to model e.g. signal processing, chemical processing and economics. A study is conducted on linear time-invariant systems, their solution and three key properties they have: Observability, reachability and stability. Three algorithms, Gaussian elimination, singular value decomposition and $QR$ decomposition, are studied for their effectiveness to determine whether a system is reachable and/or observable, and examples are given to show why the singular value decomposition is the preferred method.
- Popular Abstract (Swedish)
- Linjära tids-invarianta system är ordinära differential ekvation system som förekommer inom Reglerteknik där de används för att modellera blandt annat signal-processering, kemiska processer och ekonomi. Ett studie utförs på linjära tids-invarianta system, deras lösningar och tre nyckel egenskaper som de besitter: Observabilitet, åtkomlighet, och stabilitet. Tre algoritmer, Gaussian elimination, singular värde dekomposition och QR dekomposition studeras för att bedömma om ett system är åtkomligt och/eller observerbart, och exempel ges för att visa varför singularvärde dekomposition är den föredragna metoden.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/8997643
- author
- Óskarsson, Hallgrímur LU
- supervisor
-
- Claus Führer LU
- organization
- alternative title
- Methods of Reachability, Observability and Stability. Some Theoretical and Practical Aspects.
- course
- NUMK01 20181
- year
- 2019
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFNA-4029-2019
- ISSN
- 1654-6229
- other publication id
- 2019:K26
- language
- English
- id
- 8997643
- date added to LUP
- 2022-10-26 15:54:54
- date last changed
- 2022-10-31 12:55:02
@misc{8997643, abstract = {{Linear time-invariant systems are ordinary differential equation systems that arise in control engineering where they are used to model e.g. signal processing, chemical processing and economics. A study is conducted on linear time-invariant systems, their solution and three key properties they have: Observability, reachability and stability. Three algorithms, Gaussian elimination, singular value decomposition and $QR$ decomposition, are studied for their effectiveness to determine whether a system is reachable and/or observable, and examples are given to show why the singular value decomposition is the preferred method.}}, author = {{Óskarsson, Hallgrímur}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{On Discrete Linear Systems}}, year = {{2019}}, }