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Conference Paper: On the Mahler measure of matrix pencils

TitleOn the Mahler measure of matrix pencils
Authors
KeywordsAugmented matrices
Eigenvalue analysis
LMI-condition
Matrix pencil
Parameter-dependent Lyapunov functions
Stabilizability conditions
Uncertain parameters
Upper Bound
Issue Date2013
PublisherAmerican Automatic Control Council. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000030
Citation
The 2013 American Control Conference (ACC), Washington, DC., 17-19 June 2013. In American Control Conference Proceedings, 2013, p. 5098-5103 How to Cite?
AbstractIt is well-known that determining the Mahler measure is important in networked control systems. Indeed, this measure allows one to derive stabilizability conditions in such systems. This paper investigates the Mahler measure in networked control systems linearly affected by a single uncertain parameter constrained into an interval, i.e. systems described by a matrix pencil. It is shown that conditions for establishing an upper bound of the largest Mahler measure over the matrix pencil can be formulated through linear matrix inequalities (LMIs). In particular, two LMI conditions are proposed, one based on the construction of a parameter-dependent Lyapunov function, and another based on eigenvalue analysis through the determinants of augmented matrices. The proposed LMI conditions have the advantage to be exact, i.e. they are sufficient for any size of the LMIs and they are also necessary for a certain size of the LMIs which is known a priori. © 2013 AACC American Automatic Control Council.
Persistent Identifierhttp://hdl.handle.net/10722/184987
ISBN
ISSN

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.date.accessioned2013-07-15T10:22:16Z-
dc.date.available2013-07-15T10:22:16Z-
dc.date.issued2013en_US
dc.identifier.citationThe 2013 American Control Conference (ACC), Washington, DC., 17-19 June 2013. In American Control Conference Proceedings, 2013, p. 5098-5103en_US
dc.identifier.isbn978-1-4799-0178-4-
dc.identifier.issn0743-1619-
dc.identifier.urihttp://hdl.handle.net/10722/184987-
dc.description.abstractIt is well-known that determining the Mahler measure is important in networked control systems. Indeed, this measure allows one to derive stabilizability conditions in such systems. This paper investigates the Mahler measure in networked control systems linearly affected by a single uncertain parameter constrained into an interval, i.e. systems described by a matrix pencil. It is shown that conditions for establishing an upper bound of the largest Mahler measure over the matrix pencil can be formulated through linear matrix inequalities (LMIs). In particular, two LMI conditions are proposed, one based on the construction of a parameter-dependent Lyapunov function, and another based on eigenvalue analysis through the determinants of augmented matrices. The proposed LMI conditions have the advantage to be exact, i.e. they are sufficient for any size of the LMIs and they are also necessary for a certain size of the LMIs which is known a priori. © 2013 AACC American Automatic Control Council.-
dc.languageengen_US
dc.publisherAmerican Automatic Control Council. The Journal's web site is located at http://ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000030-
dc.relation.ispartofAmerican Control Conference Proceedingsen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectAugmented matrices-
dc.subjectEigenvalue analysis-
dc.subjectLMI-condition-
dc.subjectMatrix pencil-
dc.subjectParameter-dependent Lyapunov functions-
dc.subjectStabilizability conditions-
dc.subjectUncertain parameters-
dc.subjectUpper Bound-
dc.titleOn the Mahler measure of matrix pencilsen_US
dc.typeConference_Paperen_US
dc.identifier.emailChesi, G: chesi@eee.hku.hken_US
dc.identifier.authorityChesi, G=rp00100en_US
dc.description.naturepublished_or_final_version-
dc.identifier.scopuseid_2-s2.0-84883502757-
dc.identifier.hkuros216396en_US
dc.identifier.spage5098-
dc.identifier.epage5103-
dc.publisher.placeUnited States-
dc.customcontrol.immutablesml 140122-

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