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Article: Characterizing the solution set of polynomial systems in terms of homogeneous forms: An LMI approach

TitleCharacterizing the solution set of polynomial systems in terms of homogeneous forms: An LMI approach
Authors
KeywordsConvex Optimization
Homogeneous Forms
Linear Matrix Inequalities
Polynomial Systems
Issue Date2003
PublisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/5510
Citation
International Journal Of Robust And Nonlinear Control, 2003, v. 13 n. 13, p. 1239-1257 How to Cite?
AbstractThis paper considers the problem of determining the solution set of polynomial systems, a well-known problem in control system analysis and design. A novel approach is developed as a viable alternative to the commonly employed algebraic geometry and homotopy methods. The first result of the paper shows that the solution set of the polynomial system belongs to the kernel of a suitable symmetric matrix. Such a matrix is obtained via the solution of a linear matrix inequality (LMI) involving the maximization of the minimum eigenvalue of an affine family of symmetric matrices. The second result concerns the computation of the solution set from the kernel of the obtained matrix. For polynomial systems of degree m in n variables, a basic procedure is available if the kernel dimension does not exceed m + 1, while an extended procedure can be applied if the kernel dimension is less than n(m - 1) + 2. Finally, some application examples are illustrated to show the features of the approach and to make a brief comparison with polynomial resultant techniques. Copyright © 2003 John Wiley & Sons, Ltd.
Persistent Identifierhttp://hdl.handle.net/10722/155228
ISSN
2015 Impact Factor: 2.527
2015 SCImago Journal Rankings: 2.134
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorChesi, Gen_US
dc.contributor.authorGarulli, Aen_US
dc.contributor.authorTesi, Aen_US
dc.contributor.authorVicino, Aen_US
dc.date.accessioned2012-08-08T08:32:27Z-
dc.date.available2012-08-08T08:32:27Z-
dc.date.issued2003en_US
dc.identifier.citationInternational Journal Of Robust And Nonlinear Control, 2003, v. 13 n. 13, p. 1239-1257en_US
dc.identifier.issn1049-8923en_US
dc.identifier.urihttp://hdl.handle.net/10722/155228-
dc.description.abstractThis paper considers the problem of determining the solution set of polynomial systems, a well-known problem in control system analysis and design. A novel approach is developed as a viable alternative to the commonly employed algebraic geometry and homotopy methods. The first result of the paper shows that the solution set of the polynomial system belongs to the kernel of a suitable symmetric matrix. Such a matrix is obtained via the solution of a linear matrix inequality (LMI) involving the maximization of the minimum eigenvalue of an affine family of symmetric matrices. The second result concerns the computation of the solution set from the kernel of the obtained matrix. For polynomial systems of degree m in n variables, a basic procedure is available if the kernel dimension does not exceed m + 1, while an extended procedure can be applied if the kernel dimension is less than n(m - 1) + 2. Finally, some application examples are illustrated to show the features of the approach and to make a brief comparison with polynomial resultant techniques. Copyright © 2003 John Wiley & Sons, Ltd.en_US
dc.languageengen_US
dc.publisherJohn Wiley & Sons Ltd. The Journal's web site is located at http://www3.interscience.wiley.com/cgi-bin/jhome/5510en_US
dc.relation.ispartofInternational Journal of Robust and Nonlinear Controlen_US
dc.subjectConvex Optimizationen_US
dc.subjectHomogeneous Formsen_US
dc.subjectLinear Matrix Inequalitiesen_US
dc.subjectPolynomial Systemsen_US
dc.titleCharacterizing the solution set of polynomial systems in terms of homogeneous forms: An LMI approachen_US
dc.typeArticleen_US
dc.identifier.emailChesi, G:chesi@eee.hku.hken_US
dc.identifier.authorityChesi, G=rp00100en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1002/rnc.839en_US
dc.identifier.scopuseid_2-s2.0-0345308465en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0345308465&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume13en_US
dc.identifier.issue13en_US
dc.identifier.spage1239en_US
dc.identifier.epage1257en_US
dc.identifier.isiWOS:000186752200005-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridChesi, G=7006328614en_US
dc.identifier.scopusauthoridGarulli, A=7003697493en_US
dc.identifier.scopusauthoridTesi, A=7007124648en_US
dc.identifier.scopusauthoridVicino, A=7006250298en_US

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