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Representing externally positive systems through minimal eventually positive realizations
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0003-4142-6502
2015 (English)In: Proceedings of the IEEE 54th Annual Conference on Decision and Control (CDC),, Institute of Electrical and Electronics Engineers (IEEE), 2015, 6385-6390 p.Conference paper (Refereed)
Abstract [en]

In order to investigate the cases in which an externally positive discrete-time system fails to have a minimal positive realization, in this paper we introduce the notion of minimal eventually positive realization, fr which the state update matrix becomes positive after a certain power. This property captures 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. It is shown in the paper that whenever a minimal eventually positive realization exists, then the sequence of Markov parameters of the impulse response admits decimated subsequences for which minimal positive realizations exist and can be obtained by downsampling the eventually positive realization.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2015. 6385-6390 p.
, IEEE Conference on Decision and Control. Proceedings, ISSN 0743-1546
Keyword [en]
positive linear systems; minimal realization;eventually positive matrices; Perron-Frobenius theorem.
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-127606DOI: 10.1109/CDC.2015.7403225ISBN: 978-147997886-1OAI: diva2:925892
Conference on Decision and Control
Available from: 2016-05-03 Created: 2016-05-03 Last updated: 2016-06-10Bibliographically approved

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Altafini, Claudio
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Automatic ControlFaculty of Science & Engineering
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