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The Gram matrix allows to compute a lower bound of the minimum of a form via an LMI (linear matrix inequality) optimization by exploiting SOS (sum of squares) relaxations. This paper introduces and characterizes the Gram-tight forms, i.e. forms whose minimum coincides with this lower bound. In particular, it is shown that one can establish that a form is Gram-tight just by checking whether the dimension of the null space of the matrix returned by the LMI solver belongs to a certain range. This fact is not only theoretically interesting but has also useful applications as shown by examples with uncertain systems and nonlinear systems.
Published in:
Circuits and Systems II: Express Briefs, IEEE Transactions on
(Volume:55
,
Issue:
12
)
Date of Publication: Dec. 2008
- Page(s):
- 1299 - 1303
- ISSN :
- 1549-7747
- INSPEC Accession Number:
- 10370030
- Digital Object Identifier :
- 10.1109/TCSII.2008.2008072
- Product Type:
- Journals & Magazines
- Date of Current Version :
- 22 December 2008
- Issue Date :
- Dec. 2008
- Sponsored by :
- IEEE Circuits and Systems Society
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