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Robust stability analysis of uncertain Linear Positive Systems via Integral Linear Constraints: L-1- and L-infinity-gain characterizations
KTH, School of Electrical Engineering (EES), Communication Networks. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
2011 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Copositive Lyapunov functions are used along with dissipativity theory for stability analysis of uncertain linear positive systems. At the difference of standard results, linear supply-rates are employed for robustness and performance analysis and lead to L-1- and L-infinity-gain characterizations. This naturally guides to the definition of Integral Linear Constraints (ILCs) for the characterization of input-output nonnegative uncertainties. It turns out that these integral linear constraints can be linked to the Laplace domain, in order to be tuned adequately, by exploiting the L-1-norm and input/output signals properties. This dual viewpoint allows to prove that the static-gain of the uncertainties, only, is critical for stability. This fact provides a new explanation for the surprising stability properties of linear positive time-delay systems. The obtained stability and performance analysis conditions are expressed in terms of (robust) linear programming problems that are transformed into finite dimensional ones using the Handelman's Theorem. Several examples are provided for illustration.

Place, publisher, year, edition, pages
New York: IEEE , 2011. 6337-6342 p.
Series
Proceedings of the IEEE Conference on Decision and Control
Keyword [en]
Positive linear systems, Integral Linear Constraints, Robustness, Robust linear programming
National Category
Electrical Engineering, Electronic Engineering, Information Engineering
Identifiers
URN: urn:nbn:se:kth:diva-121647DOI: 10.1109/CDC.2011.6160194ISI: 000303506206156Scopus ID: 2-s2.0-84860654308OAI: oai:DiVA.org:kth-121647DiVA: diva2:627576
Conference
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011; Orlando, FL
Note

QC 20130612

Available from: 2013-06-12 Created: 2013-05-03 Last updated: 2013-06-12Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
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  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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  • asciidoc
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