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Conference Paper: An LMIbased approach for characterizing the solution set of polynomial systems
Title  An LMIbased approach for characterizing the solution set of polynomial systems 

Authors  
Issue Date  2000 
Citation  Proceedings Of The Ieee Conference On Decision And Control, 2000, v. 2, p. 15011506 How to Cite? 
Abstract  This 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 Identifier  http://hdl.handle.net/10722/158288 
ISSN  
References 
DC Field  Value  Language 

dc.contributor.author  Chesi, G  en_US 
dc.contributor.author  Garulli, A  en_US 
dc.contributor.author  Tesi, A  en_US 
dc.contributor.author  Vicino, A  en_US 
dc.date.accessioned  20120808T08:58:54Z   
dc.date.available  20120808T08:58:54Z   
dc.date.issued  2000  en_US 
dc.identifier.citation  Proceedings Of The Ieee Conference On Decision And Control, 2000, v. 2, p. 15011506  en_US 
dc.identifier.issn  01912216  en_US 
dc.identifier.uri  http://hdl.handle.net/10722/158288   
dc.description.abstract  This 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.language  eng  en_US 
dc.relation.ispartof  Proceedings of the IEEE Conference on Decision and Control  en_US 
dc.title  An LMIbased approach for characterizing the solution set of polynomial systems  en_US 
dc.type  Conference_Paper  en_US 
dc.description.nature  link_to_subscribed_fulltext  en_US 
dc.identifier.scopus  eid_2s2.00034439590  en_US 
dc.relation.references  http://www.scopus.com/mlt/select.url?eid=2s2.00034439590&selection=ref&src=s&origin=recordpage  en_US 
dc.identifier.volume  2  en_US 
dc.identifier.spage  1501  en_US 
dc.identifier.epage  1506  en_US 