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Article: Generalizations and new proof of the discrete-time positive real lemma and bounded real lemma

TitleGeneralizations and new proof of the discrete-time positive real lemma and bounded real lemma
Authors
Issue Date1999
Citation
Ieee Transactions On Circuits And Systems I: Fundamental Theory And Applications, 1999, v. 46 n. 6, p. 740-743 How to Cite?
AbstractThere are three different restatements claimed to be equivalent to the definition of discrete-time positive realness (DTPR) in the literature. These restatements were obtained by assuming that they are similar to the results of continuous-time positive realness when the transfer function has poles on the stability boundary. In this paper it is shown that only one of them is equivalent to the DTPR lemma and others are disproved by counter-examples. Furthermore, the DTPR lemma is specialized for minimal systems which have all poles on the unit cycle, the DTPR lemma is also generalized for nonminimal systems, the discrete-time bounded real (DTBR) lemma is proven by a simple method, and then the DTBR lemma is extended to the nonminimal case. Continuous-time results are also briefly considered in the Appendix.
Persistent Identifierhttp://hdl.handle.net/10722/169667
ISSN
2006 Impact Factor: 1.139
2006 SCImago Journal Rankings: 1.111
References

 

DC FieldValueLanguage
dc.contributor.authorXiao, Cen_US
dc.contributor.authorHill, DJen_US
dc.date.accessioned2012-10-25T04:54:05Z-
dc.date.available2012-10-25T04:54:05Z-
dc.date.issued1999en_US
dc.identifier.citationIeee Transactions On Circuits And Systems I: Fundamental Theory And Applications, 1999, v. 46 n. 6, p. 740-743en_US
dc.identifier.issn1057-7122en_US
dc.identifier.urihttp://hdl.handle.net/10722/169667-
dc.description.abstractThere are three different restatements claimed to be equivalent to the definition of discrete-time positive realness (DTPR) in the literature. These restatements were obtained by assuming that they are similar to the results of continuous-time positive realness when the transfer function has poles on the stability boundary. In this paper it is shown that only one of them is equivalent to the DTPR lemma and others are disproved by counter-examples. Furthermore, the DTPR lemma is specialized for minimal systems which have all poles on the unit cycle, the DTPR lemma is also generalized for nonminimal systems, the discrete-time bounded real (DTBR) lemma is proven by a simple method, and then the DTBR lemma is extended to the nonminimal case. Continuous-time results are also briefly considered in the Appendix.en_US
dc.languageengen_US
dc.relation.ispartofIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applicationsen_US
dc.titleGeneralizations and new proof of the discrete-time positive real lemma and bounded real lemmaen_US
dc.typeArticleen_US
dc.identifier.emailHill, DJ:en_US
dc.identifier.authorityHill, DJ=rp01669en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1109/81.768830en_US
dc.identifier.scopuseid_2-s2.0-0032652043en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0032652043&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume46en_US
dc.identifier.issue6en_US
dc.identifier.spage740en_US
dc.identifier.epage743en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridXiao, C=7202240414en_US
dc.identifier.scopusauthoridHill, DJ=35398599500en_US

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