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Conference Paper: An LMI-based approach for characterizing the solution set of polynomial systems

TitleAn LMI-based approach for characterizing the solution set of polynomial systems
Authors
Issue Date2000
Citation
Proceedings Of The Ieee Conference On Decision And Control, 2000, v. 2, p. 1501-1506 How to Cite?
AbstractThis paper considers the problem of solving certain classes of polynomial systems. This is a well known problem in control system analysis and design. A novel approach is developed as a possible 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 symmetric matrix. Such a matrix is obtained via the solution of a suitable 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 solutions from the kernel of the obtained matrix. In particular, it is shown that the solutions can be recovered quite easily if the dimension of the kernel is smaller than the degree of the polynomial system. Finally, some application examples are illustrated to show the features of the approach and to make a brief comparison with the algebraic geometry techniques.
Persistent Identifierhttp://hdl.handle.net/10722/158288
ISSN
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.accessioned2012-08-08T08:58:54Z-
dc.date.available2012-08-08T08:58:54Z-
dc.date.issued2000en_US
dc.identifier.citationProceedings Of The Ieee Conference On Decision And Control, 2000, v. 2, p. 1501-1506en_US
dc.identifier.issn0191-2216en_US
dc.identifier.urihttp://hdl.handle.net/10722/158288-
dc.description.abstractThis paper considers the problem of solving certain classes of polynomial systems. This is a well known problem in control system analysis and design. A novel approach is developed as a possible 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 symmetric matrix. Such a matrix is obtained via the solution of a suitable 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 solutions from the kernel of the obtained matrix. In particular, it is shown that the solutions can be recovered quite easily if the dimension of the kernel is smaller than the degree of the polynomial system. Finally, some application examples are illustrated to show the features of the approach and to make a brief comparison with the algebraic geometry techniques.en_US
dc.languageengen_US
dc.relation.ispartofProceedings of the IEEE Conference on Decision and Controlen_US
dc.titleAn LMI-based approach for characterizing the solution set of polynomial systemsen_US
dc.typeConference_Paperen_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.scopuseid_2-s2.0-0034439590en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-0034439590&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume2en_US
dc.identifier.spage1501en_US
dc.identifier.epage1506en_US

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