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Article: H ∞ positive filtering for positive linear discrete-time systems: An augmentation approach
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TitleH ∞ positive filtering for positive linear discrete-time systems: An augmentation approach
 
AuthorsLi, P1
Lam, J1
Shu, Z2
 
KeywordsDiscrete-time systems
H ∞ filtering
linear matrix inequality
positive filtering
positive systems
 
Issue Date2010
 
PublisherIEEE.
 
CitationIeee Transactions On Automatic Control, 2010, v. 55 n. 10, p. 2337-2342 [How to Cite?]
DOI: http://dx.doi.org/10.1109/TAC.2010.2053471
 
AbstractIn this note, we address the reduced-order positive filtering problem of positive discrete-time systems under the H ∞ performance. Commonly employed approaches, such as linear transformation and elimination technique, may not be applicable in general due to the positivity constraint of the filter. To cope with the difficulty, we first represent the filtering error system as a singular system by means of the system augmentation approach, which will facilitate the consideration of the positivity constraint. Two necessary and sufficient conditions are obtained in terms of matrix inequalities under which the filtering error system has a prescribed H ∞ performance. Then, a necessary and sufficient condition is proposed for the existence of the desired positive filters, and an iterative linear matrix inequality (LMI) algorithm is presented to compute the filtering matrices, which can be easily checked by standard software. Finally, a numerical example to illustrate the effectiveness of the proposed design procedures is presented. © 2010 IEEE.
 
ISSN0018-9286
2013 Impact Factor: 3.167
2013 SCImago Journal Rankings: 2.992
 
DOIhttp://dx.doi.org/10.1109/TAC.2010.2053471
 
ISI Accession Number IDWOS:000283362600010
Funding AgencyGrant Number
GRFHKU 7138/10E
Funding Information:

Manuscript received January 01, 2009; revised June 21, 2009, September 25, 2009, and December 10, 2009; accepted May 17, 2010. Date of publication June 21, 2010; date of current version October 06, 2010. This work was supported in part by GRF HKU 7138/10E. Recommended by Associate Editor P. Colaneri.

 
ReferencesReferences in Scopus
 
DC FieldValue
dc.contributor.authorLi, P
 
dc.contributor.authorLam, J
 
dc.contributor.authorShu, Z
 
dc.date.accessioned2011-09-23T05:49:18Z
 
dc.date.available2011-09-23T05:49:18Z
 
dc.date.issued2010
 
dc.description.abstractIn this note, we address the reduced-order positive filtering problem of positive discrete-time systems under the H ∞ performance. Commonly employed approaches, such as linear transformation and elimination technique, may not be applicable in general due to the positivity constraint of the filter. To cope with the difficulty, we first represent the filtering error system as a singular system by means of the system augmentation approach, which will facilitate the consideration of the positivity constraint. Two necessary and sufficient conditions are obtained in terms of matrix inequalities under which the filtering error system has a prescribed H ∞ performance. Then, a necessary and sufficient condition is proposed for the existence of the desired positive filters, and an iterative linear matrix inequality (LMI) algorithm is presented to compute the filtering matrices, which can be easily checked by standard software. Finally, a numerical example to illustrate the effectiveness of the proposed design procedures is presented. © 2010 IEEE.
 
dc.description.naturepublished_or_final_version
 
dc.identifier.citationIeee Transactions On Automatic Control, 2010, v. 55 n. 10, p. 2337-2342 [How to Cite?]
DOI: http://dx.doi.org/10.1109/TAC.2010.2053471
 
dc.identifier.doihttp://dx.doi.org/10.1109/TAC.2010.2053471
 
dc.identifier.epage2342
 
dc.identifier.hkuros196454
 
dc.identifier.isiWOS:000283362600010
Funding AgencyGrant Number
GRFHKU 7138/10E
Funding Information:

Manuscript received January 01, 2009; revised June 21, 2009, September 25, 2009, and December 10, 2009; accepted May 17, 2010. Date of publication June 21, 2010; date of current version October 06, 2010. This work was supported in part by GRF HKU 7138/10E. Recommended by Associate Editor P. Colaneri.

 
dc.identifier.issn0018-9286
2013 Impact Factor: 3.167
2013 SCImago Journal Rankings: 2.992
 
dc.identifier.issue10
 
dc.identifier.scopuseid_2-s2.0-77957693425
 
dc.identifier.spage2337
 
dc.identifier.urihttp://hdl.handle.net/10722/139419
 
dc.identifier.volume55
 
dc.languageeng
 
dc.publisherIEEE.
 
dc.publisher.placeUnited States
 
dc.relation.ispartofIEEE Transactions on Automatic Control
 
dc.relation.referencesReferences in Scopus
 
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License
 
dc.rights©2010 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.
 
dc.subjectDiscrete-time systems
 
dc.subjectH ∞ filtering
 
dc.subjectlinear matrix inequality
 
dc.subjectpositive filtering
 
dc.subjectpositive systems
 
dc.titleH ∞ positive filtering for positive linear discrete-time systems: An augmentation approach
 
dc.typeArticle
 
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<subject>Discrete-time systems</subject>
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Author Affiliations
  1. The University of Hong Kong
  2. National University of Ireland, Maynooth