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Article: Induced l2 and generalized H2 filtering for systems with repeated scalar nonlinearities

TitleInduced l2 and generalized H2 filtering for systems with repeated scalar nonlinearities
Authors
KeywordsDiagonally dominant matrix
Generalized H2 performance
Induced l2 performance
Linear matrix inequality
Recurrent neural networks
Repeated scalar nonlinearity
Issue Date2005
PublisherIEEE.
Citation
Ieee Transactions On Signal Processing, 2005, v. 53 n. 11, p. 4215-4226 How to Cite?
AbstractThis paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks. Both induced l2 and generalized H2 indexes are introduced to evaluate the filtering performance. For a given stable discrete-time systems with repeated scalar nonlinearities, our purpose is to design a stable full-order or reduced-order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l2 or generalized H2 performance. Sufficient conditions are obtained for the existence of admissible filters. Since these conditions involve matrix equalities, the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities, which can be readily solved by using standard numerical software. If these conditions are feasible, a desired filter can be easily constructed. These filtering results are further extended to discrete-time systems with both state delay and repeated scalar nonlinearities. The techniques used in this paper are very different from those used for previous controller synthesis problems, which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix. A numerical example is provided to show the applicability of the proposed theories. © 2005 IEEE.
Persistent Identifierhttp://hdl.handle.net/10722/44929
ISSN
2015 Impact Factor: 2.624
2015 SCImago Journal Rankings: 2.004
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorGao, Hen_HK
dc.contributor.authorLam, Jen_HK
dc.contributor.authorWang, Cen_HK
dc.date.accessioned2007-10-30T06:13:41Z-
dc.date.available2007-10-30T06:13:41Z-
dc.date.issued2005en_HK
dc.identifier.citationIeee Transactions On Signal Processing, 2005, v. 53 n. 11, p. 4215-4226en_HK
dc.identifier.issn1053-587Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/44929-
dc.description.abstractThis paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete-time state equation containing a repeated scalar nonlinearity as in recurrent neural networks. Both induced l2 and generalized H2 indexes are introduced to evaluate the filtering performance. For a given stable discrete-time systems with repeated scalar nonlinearities, our purpose is to design a stable full-order or reduced-order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l2 or generalized H2 performance. Sufficient conditions are obtained for the existence of admissible filters. Since these conditions involve matrix equalities, the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities, which can be readily solved by using standard numerical software. If these conditions are feasible, a desired filter can be easily constructed. These filtering results are further extended to discrete-time systems with both state delay and repeated scalar nonlinearities. The techniques used in this paper are very different from those used for previous controller synthesis problems, which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix. A numerical example is provided to show the applicability of the proposed theories. © 2005 IEEE.en_HK
dc.format.extent416204 bytes-
dc.format.extent1802 bytes-
dc.format.extent2200 bytes-
dc.format.extent10566 bytes-
dc.format.mimetypeapplication/pdf-
dc.format.mimetypetext/plain-
dc.format.mimetypetext/plain-
dc.format.mimetypetext/plain-
dc.languageengen_HK
dc.publisherIEEE.en_HK
dc.relation.ispartofIEEE Transactions on Signal Processingen_HK
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.rights©2005 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.subjectDiagonally dominant matrixen_HK
dc.subjectGeneralized H2 performanceen_HK
dc.subjectInduced l2 performanceen_HK
dc.subjectLinear matrix inequalityen_HK
dc.subjectRecurrent neural networksen_HK
dc.subjectRepeated scalar nonlinearityen_HK
dc.titleInduced l2 and generalized H2 filtering for systems with repeated scalar nonlinearitiesen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1053-587X&volume=53&issue=11&spage=4215&epage=4226&date=2005&atitle=Induced+l/sub+2/+and+generalized+H/sub+2/+filtering+for+systems+with+repeated+scalar+nonlinearitiesen_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/TSP.2005.857009en_HK
dc.identifier.scopuseid_2-s2.0-27744535823en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-27744535823&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume53en_HK
dc.identifier.issue11en_HK
dc.identifier.spage4215en_HK
dc.identifier.epage4226en_HK
dc.identifier.isiWOS:000232838900015-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridGao, H=7402971422en_HK
dc.identifier.scopusauthoridLam, J=7201973414en_HK
dc.identifier.scopusauthoridWang, C=8337851300en_HK

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