Title :
On the Gap Between Positive Polynomials and SOS of Polynomials
Author_Institution :
Univ. of Hong Kong, Hong Kong
fDate :
6/1/2007 12:00:00 AM
Abstract :
This note investigates the gap existing between positive polynomials and sum of squares (SOS) of polynomials, which affects several analysis and synthesis tools in control systems based on polynomial SOS relaxations, and about which almost nothing is known. In particular, a matrix characterization of the PNS, that is the positive homogeneous forms that are not SOS, is proposed, which allows to show that any PNS is the vertex of an unbounded cone of PNS. Moreover, a complete parametrization of the set of PNS is introduced.
Keywords :
control system analysis; control system synthesis; matrix algebra; polynomials; control systems; matrix characterization; polynomial sum of squares relaxations,; positive polynomials; Control system synthesis; Grid computing; Linear matrix inequalities; Lyapunov method; Matrix decomposition; Performance analysis; Polynomials; Robust control; Stability; Uncertainty; Hilbert´s 17th problem; linear matrix inequality (LMI); optimization; positive polynomial; sum of squares (SOS);
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2007.899083
