Article: H ∞ positive filtering for positive linear discrete-time systems: An augmentation approach
| Title | H ∞ positive filtering for positive linear discrete-time systems: An augmentation approach | ||||
|---|---|---|---|---|---|
| Authors | Li, P1 Lam, J1 Shu, Z2 | ||||
| Keywords | Discrete-time systems H ∞ filtering linear matrix inequality positive filtering positive systems | ||||
| Issue Date | 2010 | ||||
| Publisher | IEEE. | ||||
| Citation | Ieee 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 | ||||
| Abstract | In 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. | ||||
| ISSN | 0018-9286 2011 Impact Factor: 2.11 2011 SCImago Journal Rankings: 0.097 | ||||
| DOI | http://dx.doi.org/10.1109/TAC.2010.2053471 | ||||
| ISI Accession Number ID | WOS:000283362600010
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. | ||||
| References | References in Scopus |
| dc.contributor.author | Li, P | ||||
|---|---|---|---|---|---|
| dc.contributor.author | Lam, J | ||||
| dc.contributor.author | Shu, Z | ||||
| dc.date.accessioned | 2011-09-23T05:49:18Z | ||||
| dc.date.available | 2011-09-23T05:49:18Z | ||||
| dc.date.issued | 2010 | ||||
| dc.description.abstract | In 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.nature | published_or_final_version | ||||
| dc.identifier.citation | Ieee 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.doi | http://dx.doi.org/10.1109/TAC.2010.2053471 | ||||
| dc.identifier.epage | 2342 | ||||
| dc.identifier.hkuros | 196454 | ||||
| dc.identifier.isi | WOS:000283362600010
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.issn | 0018-9286 2011 Impact Factor: 2.11 2011 SCImago Journal Rankings: 0.097 | ||||
| dc.identifier.issue | 10 | ||||
| dc.identifier.scopus | eid_2-s2.0-77957693425 | ||||
| dc.identifier.spage | 2337 | ||||
| dc.identifier.uri | http://hdl.handle.net/10722/139419 | ||||
| dc.identifier.volume | 55 | ||||
| dc.language | eng | ||||
| dc.publisher | IEEE. | ||||
| dc.publisher.place | United States | ||||
| dc.relation.ispartof | IEEE Transactions on Automatic Control | ||||
| dc.relation.references | References in Scopus | ||||
| dc.rights | Creative 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.subject | Discrete-time systems | ||||
| dc.subject | H ∞ filtering | ||||
| dc.subject | linear matrix inequality | ||||
| dc.subject | positive filtering | ||||
| dc.subject | positive systems | ||||
| dc.title | H ∞ positive filtering for positive linear discrete-time systems: An augmentation approach | ||||
| dc.type | Article |
Author Affiliations
- The University of Hong Kong
- National University of Ireland, Maynooth