File Download
There are no files associated with this item.
Supplementary

Citations:
 Appears in Collections:
Article: Optimal representation matrices for solving polynomial systems via LMI
Title  Optimal representation matrices for solving polynomial systems via LMI 

Authors  
Keywords  System of polynomial equations and inequalities Linear matrix inequality (LMI) Square matricial representation (SMR) Control systems 
Issue Date  2008 
Publisher  Academic Publications. The Journal's web site is located at http://www.ijpam.eu/index.html 
Citation  International Journal of Pure and Applied Mathematics, 2008, v. 45 n. 3, p. 397412 How to Cite? 
Abstract  It is known that LMI can be useful for solving systems of polynomial equations and inequalities provided that the dimensions of the null spaces of some matrices representing the systems are smaller than certain thresholds. The first contribution of this paper is to show that, unfortunately, there always exist representation matrices obtainable in the LMI optimization for which these dimensions are larger than the allowed thresholds and, consequently, the extraction mechanism of the sought solutions cannot be performed. Moreover, it is also shown that, if there exist representation matrices for which these dimensions are smaller than the allowed thresholds, then these matrices can be arbitrarily illconditioned since the smallest nonzero eigenvalue can be arbitrarily close to zero, hence affecting the computation of the null spaces. Another contribution is to show that an upper bound to the dimension of these null
spaces can be imposed in a nonconservative way by adding suitable LMIs. This allows one to obtain the null spaces with the smallest dimension via a finite sequence of feasibility tests. Moreover, the introduced LMIs also allow to avoid illconditioned representation matrices, if possible, by simply turning the feasible tests into suitable convex maximizations. 
Persistent Identifier  http://hdl.handle.net/10722/73540 
ISSN  2015 SCImago Journal Rankings: 0.299 
DC Field  Value  Language 

dc.contributor.author  Chesi, G  en_HK 
dc.date.accessioned  20100906T06:52:20Z   
dc.date.available  20100906T06:52:20Z   
dc.date.issued  2008  en_HK 
dc.identifier.citation  International Journal of Pure and Applied Mathematics, 2008, v. 45 n. 3, p. 397412  en_HK 
dc.identifier.issn  13118080  en_HK 
dc.identifier.uri  http://hdl.handle.net/10722/73540   
dc.description.abstract  It is known that LMI can be useful for solving systems of polynomial equations and inequalities provided that the dimensions of the null spaces of some matrices representing the systems are smaller than certain thresholds. The first contribution of this paper is to show that, unfortunately, there always exist representation matrices obtainable in the LMI optimization for which these dimensions are larger than the allowed thresholds and, consequently, the extraction mechanism of the sought solutions cannot be performed. Moreover, it is also shown that, if there exist representation matrices for which these dimensions are smaller than the allowed thresholds, then these matrices can be arbitrarily illconditioned since the smallest nonzero eigenvalue can be arbitrarily close to zero, hence affecting the computation of the null spaces. Another contribution is to show that an upper bound to the dimension of these null spaces can be imposed in a nonconservative way by adding suitable LMIs. This allows one to obtain the null spaces with the smallest dimension via a finite sequence of feasibility tests. Moreover, the introduced LMIs also allow to avoid illconditioned representation matrices, if possible, by simply turning the feasible tests into suitable convex maximizations.   
dc.language  eng  en_HK 
dc.publisher  Academic Publications. The Journal's web site is located at http://www.ijpam.eu/index.html  en_HK 
dc.relation.ispartof  International Journal of Pure and Applied Mathematics  en_HK 
dc.subject  System of polynomial equations and inequalities   
dc.subject  Linear matrix inequality (LMI)   
dc.subject  Square matricial representation (SMR)   
dc.subject  Control systems   
dc.title  Optimal representation matrices for solving polynomial systems via LMI  en_HK 
dc.type  Article  en_HK 
dc.identifier.openurl  http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=13118080&volume=&spage=397&epage=412&date=2008&atitle=Optimal+representation+matrices+for+solving+polynomial+systems+via+LMI  en_HK 
dc.identifier.email  Chesi, G: chesi@eee.hku.hk  en_HK 
dc.identifier.authority  Chesi, G=rp00100  en_HK 
dc.description.nature  link_to_subscribed_fulltext   
dc.identifier.hkuros  149165  en_HK 
dc.identifier.volume  45   
dc.identifier.issue  3   
dc.identifier.spage  397   
dc.identifier.epage  412   
dc.publisher.place  Bulgaria   