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On Discrete Linear Systems

Óskarsson, Hallgrímur LU (2019) In Bachelor's Theses in Mathematical Sciences NUMK01 20181
Mathematics (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:
author
Óskarsson, Hallgrímur LU
supervisor
organization
alternative title
Methods of Reachability, Observability and Stability. Some Theoretical and Practical Aspects.
course
NUMK01 20181
year
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}},
}