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Article: On the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equation
Title | On the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equation |
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Authors | |
Keywords | 2-D Analog Systems 2-D Continuous-Time Lyapunov Equation Very Strict Positive Realness |
Issue Date | 1997 |
Publisher | Springer 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? |
Abstract | The 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 Identifier | http://hdl.handle.net/10722/169650 |
ISSN | 2023 Impact Factor: 1.7 2023 SCImago Journal Rankings: 0.499 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Xiao, C | en_US |
dc.contributor.author | Agathoklis, P | en_US |
dc.contributor.author | Hill, DJ | en_US |
dc.date.accessioned | 2012-10-25T04:54:01Z | - |
dc.date.available | 2012-10-25T04:54:01Z | - |
dc.date.issued | 1997 | en_US |
dc.identifier.citation | Multidimensional Systems And Signal Processing, 1997, v. 8 n. 3, p. 315-333 | en_US |
dc.identifier.issn | 0923-6082 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/169650 | - |
dc.description.abstract | The 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.language | eng | en_US |
dc.publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0923-6082 | en_US |
dc.relation.ispartof | Multidimensional Systems and Signal Processing | en_US |
dc.subject | 2-D Analog Systems | en_US |
dc.subject | 2-D Continuous-Time Lyapunov Equation | en_US |
dc.subject | Very Strict Positive Realness | en_US |
dc.title | On the Positive Definite Solutions to the 2-D Continuous-time Lyapunov Equation | en_US |
dc.type | Article | en_US |
dc.identifier.email | Hill, DJ: | en_US |
dc.identifier.authority | Hill, DJ=rp01669 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.scopus | eid_2-s2.0-0031185349 | en_US |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-0031185349&selection=ref&src=s&origin=recordpage | en_US |
dc.identifier.volume | 8 | en_US |
dc.identifier.issue | 3 | en_US |
dc.identifier.spage | 315 | en_US |
dc.identifier.epage | 333 | en_US |
dc.identifier.isi | WOS:A1997XE48600005 | - |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Xiao, C=7202240414 | en_US |
dc.identifier.scopusauthorid | Agathoklis, P=7005622057 | en_US |
dc.identifier.scopusauthorid | Hill, DJ=35398599500 | en_US |
dc.identifier.issnl | 0923-6082 | - |