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Article: Robust stability and stabilization of discrete singular systems: An equivalent characterization

TitleRobust stability and stabilization of discrete singular systems: An equivalent characterization
Authors
KeywordsDiscrete-time systems
Linear matrix inequality (LMI)
Parameter uncertainty
Robust stability
Robust stabilization
Singular systems
Issue Date2004
PublisherIEEE.
Citation
Ieee Transactions On Automatic Control, 2004, v. 49 n. 4, p. 568-573 How to Cite?
AbstractThis note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.
Persistent Identifierhttp://hdl.handle.net/10722/43065
ISSN
2015 Impact Factor: 2.777
2015 SCImago Journal Rankings: 4.238
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorXu, Sen_HK
dc.contributor.authorLam, Jen_HK
dc.date.accessioned2007-03-23T04:37:59Z-
dc.date.available2007-03-23T04:37:59Z-
dc.date.issued2004en_HK
dc.identifier.citationIeee Transactions On Automatic Control, 2004, v. 49 n. 4, p. 568-573en_HK
dc.identifier.issn0018-9286en_HK
dc.identifier.urihttp://hdl.handle.net/10722/43065-
dc.description.abstractThis note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.en_HK
dc.format.extent223594 bytes-
dc.format.extent35328 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypeapplication/msword-
dc.languageengen_HK
dc.publisherIEEE.en_HK
dc.relation.ispartofIEEE Transactions on Automatic Controlen_HK
dc.rights©2004 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.en_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectDiscrete-time systemsen_HK
dc.subjectLinear matrix inequality (LMI)en_HK
dc.subjectParameter uncertaintyen_HK
dc.subjectRobust stabilityen_HK
dc.subjectRobust stabilizationen_HK
dc.subjectSingular systemsen_HK
dc.titleRobust stability and stabilization of discrete singular systems: An equivalent characterizationen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0018-9286&volume=49&issue=4&spage=568&epage=574&date=2004&atitle=Robust+stability+and+stabilization+of+discrete+singular+systems:+an+equivalent+characterizationen_HK
dc.identifier.emailLam, J:james.lam@hku.hken_HK
dc.identifier.authorityLam, J=rp00133en_HK
dc.description.naturepublished_or_final_versionen_HK
dc.identifier.doi10.1109/TAC.2003.822854en_HK
dc.identifier.scopuseid_2-s2.0-2442543340en_HK
dc.identifier.hkuros90753-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-2442543340&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume49en_HK
dc.identifier.issue4en_HK
dc.identifier.spage568en_HK
dc.identifier.epage573en_HK
dc.identifier.isiWOS:000220884800009-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridXu, S=7404438591en_HK
dc.identifier.scopusauthoridLam, J=7201973414en_HK

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