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Article: Optimal time-weighted H2 model reduction for Markovian jump systems

TitleOptimal time-weighted H2 model reduction for Markovian jump systems
Authors
KeywordsComputational procedures
Error systems
Gradient flow
H2 norm
Jump system
Issue Date2012
PublisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207179.asp
Citation
International Journal of Control, 2012, v. 85 n. 6, p. 613-628 How to Cite?
AbstractThis article addresses the optimal time-weighted H 2 model reduction problem for Markovian jump linear systems. That is, for a given mean square stable Markovian jump system, our aim is to find a mean square stable jump system of lower order such that the time-weighted H 2 norm of the corresponding error system is minimised. The time-weighted H 2 norm of the system is first defined, and then a computational method is constructed. The computation requires the solution of two sets of recursive Lyapunov-type linear matrix equations associated with the Markovian jump system. To solve the optimal time-weighted H 2 model reduction problem, we propose a gradient flow method for its solution. A necessary condition for minimality is derived, and a computational procedure is provided to obtain the minimising reduced-order model. The necessary condition generalises the standard result for systems when Markov jumps and the time-weighting term do not appear. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed approach. © 2012 Taylor & Francis.
Persistent Identifierhttp://hdl.handle.net/10722/157206
ISSN
2015 Impact Factor: 1.88
2015 SCImago Journal Rankings: 1.494
ISI Accession Number ID
Funding AgencyGrant Number
Fundamental Research Funds for the Central Universities, China201013036
SRFDP, China20110132120013
GRF HKU7137/09E
NSFC61074043
Qing Lan Project
Funding Information:

This work was partially supported by the Fundamental Research Funds for the Central Universities, China, under Grant 201013036, by SRFDP, China, under Grant 20110132120013, by GRF HKU 7137/09E, by NSFC 61074043 and the Qing Lan Project.

References

 

DC FieldValueLanguage
dc.contributor.authorSun, Men_US
dc.contributor.authorLam, Jen_US
dc.contributor.authorXu, Sen_US
dc.contributor.authorShu, Zen_US
dc.date.accessioned2012-08-08T08:45:49Z-
dc.date.available2012-08-08T08:45:49Z-
dc.date.issued2012en_US
dc.identifier.citationInternational Journal of Control, 2012, v. 85 n. 6, p. 613-628en_US
dc.identifier.issn0020-7179en_US
dc.identifier.urihttp://hdl.handle.net/10722/157206-
dc.description.abstractThis article addresses the optimal time-weighted H 2 model reduction problem for Markovian jump linear systems. That is, for a given mean square stable Markovian jump system, our aim is to find a mean square stable jump system of lower order such that the time-weighted H 2 norm of the corresponding error system is minimised. The time-weighted H 2 norm of the system is first defined, and then a computational method is constructed. The computation requires the solution of two sets of recursive Lyapunov-type linear matrix equations associated with the Markovian jump system. To solve the optimal time-weighted H 2 model reduction problem, we propose a gradient flow method for its solution. A necessary condition for minimality is derived, and a computational procedure is provided to obtain the minimising reduced-order model. The necessary condition generalises the standard result for systems when Markov jumps and the time-weighting term do not appear. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed approach. © 2012 Taylor & Francis.en_US
dc.languageengen_US
dc.publisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00207179.aspen_US
dc.relation.ispartofInternational Journal of Controlen_US
dc.subjectComputational proceduresen_US
dc.subjectError systemsen_US
dc.subjectGradient flowen_US
dc.subjectH2 normen_US
dc.subjectJump system-
dc.titleOptimal time-weighted H2 model reduction for Markovian jump systemsen_US
dc.typeArticleen_US
dc.identifier.emailLam, J: james.lam@hku.hken_US
dc.identifier.authorityLam, J=rp00133en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1080/00207179.2012.661081en_US
dc.identifier.scopuseid_2-s2.0-84862094108en_US
dc.identifier.hkuros212135-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-84862094108&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume85en_US
dc.identifier.issue6en_US
dc.identifier.spage613en_US
dc.identifier.epage628en_US
dc.identifier.isiWOS:000303543700001-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridShu, Z=54899441200en_US
dc.identifier.scopusauthoridXu, S=55247191700en_US
dc.identifier.scopusauthoridLam, J=7201973414en_US
dc.identifier.scopusauthoridSun, M=8644986100en_US

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