Positivstellensatz for Trigonometric Polynomials and Multidimensional Stability Tests

Author

Dumitrescu, Bogdan

Author_Institution

Tampere Int. Center for Signal Process., Tampere Univ. of Technol.

Volume

54

Issue

4

fYear

2007

fDate

4/1/2007 12:00:00 AM

Firstpage

353

Lastpage

356

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;

fLanguage

English

Journal_Title

Circuits and Systems II: Express Briefs, IEEE Transactions on

Publisher

ieee

ISSN

1549-7747

Type

jour

DOI

10.1109/TCSII.2006.890409

Filename

4155059