Balanced truncation for linear switched systems

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dc.citation.journalTitleAdvances in Computational Mathematicsen_US
dc.contributor.authorGosea, Ion Victoren_US
dc.contributor.authorPetreczky, Mihalyen_US
dc.contributor.authorAntoulas, Athanasios C.en_US
dc.contributor.authorFiter, Christopheen_US
dc.date.accessioned2018-08-21T16:18:44Zen_US
dc.date.available2018-08-21T16:18:44Zen_US
dc.date.issued2018en_US
dc.description.abstractWe propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians corresponding to each active discrete mode by solving systems of coupled Lyapunov equations. Depending on the type, each such Gramian corresponds to the energy associated to all possible switching scenarios that start or, respectively end, in a particular operational mode. In order to guarantee that hard to control and hard to observe states are simultaneously eliminated, we construct a transformed system, whose Gramians are equal and diagonal. Then, by truncation, directly construct reduced order models. One can show that these models preserve some properties of the original model, such as stability and that it is possible to obtain error bounds relating the observed output, the control input and the entries of the diagonal Gramians.en_US
dc.identifier.citationGosea, Ion Victor, Petreczky, Mihaly, Antoulas, Athanasios C., et al.. "Balanced truncation for linear switched systems." <i>Advances in Computational Mathematics,</i> (2018) Springer: https://doi.org/10.1007/s10444-018-9610-z.en_US
dc.identifier.digitalBalancedTruncationen_US
dc.identifier.doihttps://doi.org/10.1007/s10444-018-9610-zen_US
dc.identifier.urihttps://hdl.handle.net/1911/102480en_US
dc.language.isoengen_US
dc.publisherSpringeren_US
dc.rightsThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.en_US
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en_US
dc.subject.keywordmodel order reductionen_US
dc.subject.keywordswitched systemsen_US
dc.subject.keywordbalanced truncationen_US
dc.subject.keywordinfinite gramiansen_US
dc.subject.keywordcontrollabilityen_US
dc.subject.keywordobservabilityen_US
dc.titleBalanced truncation for linear switched systemsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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