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Article: On the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equation

TitleOn the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equation
Authors
Keywords2-D Analog Systems
2-D Continuous-Time Lyapunov Equation
Very Strict Positive Realness
Issue Date1997
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0923-6082
Citation
Multidimensional Systems And Signal Processing, 1997, v. 8 n. 3, p. 315-333 How to Cite?
AbstractThe very strict positive real lemma is further developed for nonminimal 1-D continuous-time systems and is used to study the 2-D continuous-time Lyapunov equation. Based on it, an extended condition for the bivariate characteristic polynomial of a matrix to be very strict Hurwitz is proposed for general 2-D analog systems with characteristic polynomials involving 1-D factor polynomials. It is also shown that in such a case the bivariate polynomial can be decomposed into a 2-D bivariate polynomial with the corresponding matrix satisfying certain controllability and observability conditions and into up to two 1-D polynomials. Further, two algorithms for computing the positive definite solutions to the 2-D Lyapunov equation are presented.
Persistent Identifierhttp://hdl.handle.net/10722/169650
ISSN
2015 Impact Factor: 1.436
2015 SCImago Journal Rankings: 0.768
References

 

DC FieldValueLanguage
dc.contributor.authorXiao, Cen_US
dc.contributor.authorAgathoklis, Pen_US
dc.contributor.authorHill, DJen_US
dc.date.accessioned2012-10-25T04:54:01Z-
dc.date.available2012-10-25T04:54:01Z-
dc.date.issued1997en_US
dc.identifier.citationMultidimensional Systems And Signal Processing, 1997, v. 8 n. 3, p. 315-333en_US
dc.identifier.issn0923-6082en_US
dc.identifier.urihttp://hdl.handle.net/10722/169650-
dc.description.abstractThe very strict positive real lemma is further developed for nonminimal 1-D continuous-time systems and is used to study the 2-D continuous-time Lyapunov equation. Based on it, an extended condition for the bivariate characteristic polynomial of a matrix to be very strict Hurwitz is proposed for general 2-D analog systems with characteristic polynomials involving 1-D factor polynomials. It is also shown that in such a case the bivariate polynomial can be decomposed into a 2-D bivariate polynomial with the corresponding matrix satisfying certain controllability and observability conditions and into up to two 1-D polynomials. Further, two algorithms for computing the positive definite solutions to the 2-D Lyapunov equation are presented.en_US
dc.languageengen_US
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0923-6082en_US
dc.relation.ispartofMultidimensional Systems and Signal Processingen_US
dc.subject2-D Analog Systemsen_US
dc.subject2-D Continuous-Time Lyapunov Equationen_US
dc.subjectVery Strict Positive Realnessen_US
dc.titleOn the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equationen_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.scopuseid_2-s2.0-0031185349en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0031185349&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume8en_US
dc.identifier.issue3en_US
dc.identifier.spage315en_US
dc.identifier.epage333en_US
dc.publisher.placeUnited Statesen_US
dc.identifier.scopusauthoridXiao, C=7202240414en_US
dc.identifier.scopusauthoridAgathoklis, P=7005622057en_US
dc.identifier.scopusauthoridHill, DJ=35398599500en_US

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