Balanced truncation for linear switched systems

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dc.citation.journalTitleAdvances in Computational Mathematics
dc.contributor.authorGosea, Ion Victor
dc.contributor.authorPetreczky, Mihaly
dc.contributor.authorAntoulas, Athanasios C.
dc.contributor.authorFiter, Christophe
dc.date.accessioned2018-08-21T16:18:44Z
dc.date.available2018-08-21T16:18:44Z
dc.date.issued2018
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.
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.
dc.identifier.digitalBalancedTruncation
dc.identifier.doihttps://doi.org/10.1007/s10444-018-9610-z
dc.identifier.urihttps://hdl.handle.net/1911/102480
dc.language.isoeng
dc.publisherSpringer
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.
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subject.keywordmodel order reduction
dc.subject.keywordswitched systems
dc.subject.keywordbalanced truncation
dc.subject.keywordinfinite gramians
dc.subject.keywordcontrollability
dc.subject.keywordobservability
dc.titleBalanced truncation for linear switched systems
dc.typeJournal article
dc.type.dcmiText
dc.type.publicationpublisher version
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