Robust stability analysis of uncertain Linear Positive Systems via Integral Linear Constraints: L-1- and L-infinity-gain characterizations
2011 (English)Conference paper (Refereed)
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.
, Proceedings of the IEEE Conference on Decision and Control
Positive linear systems, Integral Linear Constraints, Robustness, Robust linear programming
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-121647DOI: 10.1109/CDC.2011.6160194ISI: 000303506206156ScopusID: 2-s2.0-84860654308OAI: oai:DiVA.org:kth-121647DiVA: diva2:627576
2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011; Orlando, FL
QC 201306122013-06-122013-05-032013-06-12Bibliographically approved