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Minimal eventually positive realizations of externally positive systems
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering. (Automatic Control)ORCID iD: 0000-0003-4142-6502
2016 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 68, 140-147 p.Article in journal (Refereed) Published
Abstract [en]

It is a well-known fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. As a consequence, we show that in discrete-time it is possible to use downsampling to obtain minimal positive realizations matching decimated sequences of Markov coefficients of the impulse response. In continuous-time, instead, if the sampling time is chosen sufficiently long, a minimal eventually positive realization leads always to a sampled realization which is minimal and positive.

Place, publisher, year, edition, pages
Pergamon Press, 2016. Vol. 68, 140-147 p.
Keyword [en]
Positive linear systems;Minimal realization;Eventually positive matrices;Perron–Frobenius theorem
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-127609DOI: 10.1016/j.automatica.2016.01.072ISI: 000375507600016OAI: oai:DiVA.org:liu-127609DiVA: diva2:925899
Note

Funding agencies: Swedish Research Council [2015-04390]

Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2017-05-08Bibliographically approved

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Altafini, Claudio
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CiteExportLink to record
Permanent link

Direct link
Cite
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