DocumentCode
800871
Title
Positivity, Complete Positivity, and SOS Representation
Author
Bose, N.K.
Author_Institution
Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA
Volume
54
Issue
5
fYear
2009
fDate
5/1/2009 12:00:00 AM
Firstpage
1054
Lastpage
1057
Abstract
The gap between positive multivariate polynomials and the sum-of-squares (SOS) representation has resurfaced as a problem of importance and interest in control theory. A representation theorem for a bihermitian form is proved. A linear map and its dual are associated with this unique form. Complete positivity and not just positivity of the linear maps is necessary as well as sufficient for SOS representation of the form.
Keywords
control theory; polynomials; SOS representation; bihermitian form; control theory; linear maps; positive multivariate polynomials; representation theorem; sum-of-squares representation; Circuit testing; Control system synthesis; Control theory; Equations; Linear matrix inequalities; Output feedback; Polynomials; Robustness; Sections; System testing; Bihermitian form; complete positivity; control; optimization; polynomial positivity (nonnegativity); sum-of-squares (SOS);
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2009.2017160
Filename
4907235
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