Title :
Characterizing the positive polynomials which are not SOS
Author_Institution :
Department of Information Engineering, University of Siena, Italy chesi@dii.unisi.it
Abstract :
Several analysis and synthesis tools in control systems are based on polynomial sum of squares (SOS) relaxations. However, almost nothing is known about the gap existing between positive polynomials and SOS of polynomials. This paper investigates such a gap proposing a matrix characterization of PNS, that is homogeneous forms that are not SOS.In particular, it is shown that any PNS is the vertex of an unbounded cone of PNS. Moreover, a complete parameterization of the set of PNS is introduced.
Keywords :
Hilbert´s 17th problem; LMI; Optimization in control; Positive polynomial; SOS; Control system analysis; Control system synthesis; Convergence; Lyapunov method; Matrix decomposition; Performance analysis; Performance gain; Polynomials; Stability; Uncertainty; Hilbert´s 17th problem; LMI; Optimization in control; Positive polynomial; SOS;
Conference_Titel :
Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on
Print_ISBN :
0-7803-9567-0
DOI :
10.1109/CDC.2005.1582394
