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Conference Paper: H∞ model reduction for positive systems

TitleH∞ model reduction for positive systems
Authors
KeywordsError systems
Lyapunov matrix
Model reduction problems
Numerical example
Original systems
Issue Date2010
PublisherAmerican Automatic Control Council.
Citation
The 2010 American Control Conference (ACC2010), Baltimore, MD., 30 June-2 July 2010. In American Control Conference Proceedings, 2010, p. 6244-6249 How to Cite?
AbstractThis paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H∞ performance. Based upon a system augmentation approach, a novel characterization on the stability with H∞ performance of the error system is first obtained in terms of linear matrix inequality (LMI). Then, a necessary and sufficient condition for the existence of a desired reduced-order model is derived accordingly. A significance of the proposed approach is that the reduced-order system matrices can be parametrized by a positive definite matrix with flexible structure, which is fully independent of the Lyapunov matrix; thus, the positivity constraint on the reduced-order system can be readily embedded in the model reduction problem. Finally, a numerical example is provided to show the effectiveness of the proposed techniques.
Persistent Identifierhttp://hdl.handle.net/10722/159019
ISBN
ISSN
References

 

DC FieldValueLanguage
dc.contributor.authorLi, Pen_US
dc.contributor.authorLam, Jen_US
dc.contributor.authorWang, Zen_US
dc.date.accessioned2012-08-08T09:05:10Z-
dc.date.available2012-08-08T09:05:10Z-
dc.date.issued2010en_US
dc.identifier.citationThe 2010 American Control Conference (ACC2010), Baltimore, MD., 30 June-2 July 2010. In American Control Conference Proceedings, 2010, p. 6244-6249en_US
dc.identifier.isbn978-1-4244-7427-1-
dc.identifier.issn0743-1619-
dc.identifier.urihttp://hdl.handle.net/10722/159019-
dc.description.abstractThis paper is concerned with the model reduction of positive systems. For a given stable positive system, our attention is focused on the construction of a reduced-order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed H∞ performance. Based upon a system augmentation approach, a novel characterization on the stability with H∞ performance of the error system is first obtained in terms of linear matrix inequality (LMI). Then, a necessary and sufficient condition for the existence of a desired reduced-order model is derived accordingly. A significance of the proposed approach is that the reduced-order system matrices can be parametrized by a positive definite matrix with flexible structure, which is fully independent of the Lyapunov matrix; thus, the positivity constraint on the reduced-order system can be readily embedded in the model reduction problem. Finally, a numerical example is provided to show the effectiveness of the proposed techniques.en_US
dc.languageengen_US
dc.publisherAmerican Automatic Control Council.-
dc.relation.ispartofAmerican Control Conference Proceedingsen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectError systems-
dc.subjectLyapunov matrix-
dc.subjectModel reduction problems-
dc.subjectNumerical example-
dc.subjectOriginal systems-
dc.titleH∞ model reduction for positive systemsen_US
dc.typeConference_Paperen_US
dc.identifier.emailLam, J: james.lam@hku.hken_US
dc.identifier.authorityLam, J=rp00133en_US
dc.description.naturepublished_or_final_versionen_US
dc.identifier.scopuseid_2-s2.0-77957765610en_US
dc.identifier.hkuros179736-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-77957765610&selection=ref&src=s&origin=recordpageen_US
dc.identifier.spage6244en_US
dc.identifier.epage6249en_US
dc.publisher.placeUnited States-
dc.description.otherThe 2010 American Control Conference (ACC2010), Baltimore, MD., 30 June-2 July 2010. In American Control Conference Proceedings, 2010, p. 6244-6249-
dc.identifier.scopusauthoridWang, Z=35231712300en_US
dc.identifier.scopusauthoridLam, J=7201973414en_US
dc.identifier.scopusauthoridLi, P=35069715100en_US

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