Title :
Positivstellensatz for Trigonometric Polynomials and Multidimensional Stability Tests
Author :
Dumitrescu, Bogdan
Author_Institution :
Tampere Int. Center for Signal Process., Tampere Univ. of Technol.
fDate :
4/1/2007 12:00:00 AM
Abstract :
We propose a Positivstellensatz for trigonometric polynomials that is simpler than its correspondent for polynomials of real variable. Using it, we give a stability test for multidimensional systems, consisting of checking the feasibility of a linear matrix inequality. The same result is used for a robust stability test for systems whose coefficients depend polynomially on some bounded parameters. The new tests are either more accurate or faster than previous ones
Keywords :
linear matrix inequalities; multidimensional systems; polynomials; stability; transfer functions; Positivstellensatz; linear matrix inequality; multidimensional stability tests; multidimensional systems; robust stability; semidefinite programming; sum-of-squares polynomials; trigonometric polynomials; Circuits; Linear matrix inequalities; Linear programming; Multidimensional signal processing; Multidimensional systems; Polynomials; Robust stability; System testing; Transfer functions; Positivstellensatz; robust stability; semidefinite programming; stability; sum-of-squares polynomials;
Journal_Title :
Circuits and Systems II: Express Briefs, IEEE Transactions on
DOI :
10.1109/TCSII.2006.890409
