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Discrete-Time k-Positive Linear Systems

  • Positive systems play an important role in systems and control theory and have found applications in multiagent systems, neural networks, systems biology, and more. Positive systems map the nonnegative orthant to itself (and also the non-positive orthant to itself). In other words, they map the set of vectors with zero sign variation to itself. In this article, discrete-time linear systems that map the set of vectors with up to k-1 sign variations to itself are introduced. For the special case k = 1 these reduce to discrete-time positive linear systems. Properties of these systems are analyzed using tools from the theory of sign-regular matrices. In particular, it is shown that almost every solution of such systems converges to the set of vectors with up to k-1 sign variations. It is also shown that these systems induce a positive dynamics of k-dimensional parallelotopes.

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Metadaten
Author:Rola AlseidiORCiD, Michael MargaliotORCiD, Jürgen GarloffORCiDGND
URN:urn:nbn:de:bsz:kon4-opus4-29517
DOI:https://doi.org/10.1109/TAC.2020.2987285
ISSN:0018-9286
ISSN:1558-2523
Parent Title (English):IEEE Transactions on Automatic Control
Volume:66
Publisher:IEEE
Document Type:Article
Language:English
Year of Publication:2021
Release Date:2022/01/08
Tag:Compound matrices; Cones of rank k; Exterior products; Sign-regular matrices; Stability analysis
Issue:1
First Page:399
Last Page:405
Institutes:Institut für Angewandte Forschung - IAF
DDC functional group:500 Naturwissenschaften und Mathematik
Relevance:Peer reviewed Publikation in Master Journal List
Open Access?:Nein
Licence (German):License LogoUrheberrechtlich geschützt