Title :
Positivity, Complete Positivity, and SOS Representation
Author_Institution :
Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA
fDate :
5/1/2009 12:00:00 AM
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);
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2009.2017160
