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Long-term behavior of cross-dimensional linear dynamical systems
KTH, School of Electrical Engineering and Computer Science (EECS), Automatic Control. KTH, School of Electrical Engineering and Computer Science (EECS), Centres, ACCESS Linnaeus Centre. Harbin Engn Univ, Coll Automat, Harbin 150001, Heilongjiang, Peoples R China..
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: 2018 37th Chinese Control Conference (CCC) / [ed] Chen, X Zhao, QC, Institute of Electrical and Electronics Engineers (IEEE), 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
Institute of Electrical and Electronics Engineers (IEEE), 2018. p. 158-163
Series
Chinese Control Conference, ISSN 2161-2927
Keywords [en]
Long-term behavior, cross-dimensional vector space, cross-dimensional linear dynamical system, dimension-boundedness, basis, Drazin inverse
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-254151DOI: 10.23919/ChiCC.2018.8482746ISI: 000468622100028Scopus ID: 2-s2.0-85056129786ISBN: 978-9-8815-6395-8 (print)OAI: oai:DiVA.org:kth-254151DiVA, id: diva2:1329959
Conference
37th Chinese Control Conference, CCC 2018, Wuhan, China, 25 July 2018 through 27 July 2018
Note

QC 20190625

Available from: 2019-06-25 Created: 2019-06-25 Last updated: 2019-06-25Bibliographically approved

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Zhang, KuizeJohansson, Karl Henrik

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