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Characterizing the Positive Semidefiniteness of Signed Laplacians via Effective Resistances
KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
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2016 (English)In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Institute of Electrical and Electronics Engineers (IEEE), 2016, 985-990 p., 7798396Conference paper, Published paper (Refereed)
Abstract [en]

A symmetric signed Laplacian matrix uniquely defines a resistive electrical circuit, where the negative weights correspond to negative resistances. The positive semidefiniteness of signed Laplacian matrices is studied in this paper using the concept of effective resistance. We show that a signed Laplacian matrix is positive semidefinite with a simple zero eigenvalue if, and only if, the underlying graph is connected, and a suitably defined effective resistance matrix is positive definite.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers (IEEE), 2016. 985-990 p., 7798396
Series
IEEE Conference on Decision and Control, ISSN 0743-1546
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:kth:diva-208622DOI: 10.1109/CDC.2016.7798396ISI: 000400048101027Scopus ID: 2-s2.0-85010749037ISBN: 978-1-5090-1837-6 (print)OAI: oai:DiVA.org:kth-208622DiVA: diva2:1108026
Conference
55th IEEE Conference on Decision and Control, CDC 2016, ARIA Resort and Casino, Las Vegas, United States, 12 December 2016 through 14 December 2016
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council
Note

QC 20170612

Available from: 2017-06-12 Created: 2017-06-12 Last updated: 2017-06-12Bibliographically approved

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