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Implicitization, Graph Ideals and Control Systems
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
1993 (English)Report (Other academic)
Abstract [en]

We discuss how the external behavior of a polynomial automatic control system can be determined, i.e. how to find the differential equation relating the input and the output of the system given a state space description, focussing on algorithmic aspects. This problem is equivalent to what is known as implicitization in computational algebraic geometry and one way of doing this is to perform elimination in so called graph ideals. We compare different methods for implicitization with regard to computational complexity. Moreover, a bound for the degree of the input-output equation in terms of the degrees of the state equations is derived.

Place, publisher, year, edition, pages
Linköping: Linköping University , 1993. , 8 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 1508
Keyword [en]
Control systems, State space theory, Algebraic geometry, Implicitization, Bézout's theorem, Computer algebra, Symbolic computation, Elimination, Gröbner bases, Computational complexity
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55601ISRN: LiTH-ISY-R-1508OAI: oai:DiVA.org:liu-55601DiVA: diva2:316314
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-12Bibliographically approved

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Automatic ControlThe Institute of Technology
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CiteExportLink to record
Permanent link

Direct link
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf