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Long-term behavior of cross-dimensional linear dynamical systems
KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control.
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre.ORCID iD: 0000-0001-9940-5929
2018 (English)In: Chinese Control Conference, CCC, IEEE Computer Society , 2018, p. 158-163Conference paper, Published paper (Refereed)
Abstract [en]

Let M and V denote the sets of finite-dimensional matrices and finite-dimensional column vectors, respectively. Based on the semitensor product and the vector addition, M and V both form a monoid, where V is commutative. In addition, based on an equivalence relation ↔ on V, the induced quotient space V/ ↔ forms a vector space. In this paper, we give a basis for the vector space V/ ↔ , showing that V/ ↔ is of countably infinite dimension. In addition, we give an explicit characterization for how the dimension of a vector in V changes caused by the repetitive actions of a matrix in M on the vector, and characterize the generalized inverse behavior of the repetitive actions.

Place, publisher, year, edition, pages
IEEE Computer Society , 2018. p. 158-163
Keywords [en]
Basis, Cross-dimensional linear dynamical system, Cross-dimensional vector space, Dimension- boundedness, Drazin inverse, Long-term behavior, Dynamical systems, Linear control systems, Matrix algebra, Vectors, Boundedness, Dimensional vectors, Linear dynamical systems, Vector spaces
National Category
Computer and Information Sciences
Identifiers
URN: urn:nbn:se:kth:diva-247145DOI: 10.23919/ChiCC.2018.8482746Scopus ID: 2-s2.0-85056129786ISBN: 9789881563941 (print)OAI: oai:DiVA.org:kth-247145DiVA, id: diva2:1314024
Conference
37th Chinese Control Conference, CCC 2018, 25 July 2018 through 27 July 2018
Funder
Swedish Research CouncilKnut and Alice Wallenberg FoundationSwedish Foundation for Strategic Research
Note

QC 20190507

Available from: 2019-05-07 Created: 2019-05-07 Last updated: 2019-05-07Bibliographically approved

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Zhang, KuizeJohansson, Karl H.

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