Multidimensional stability test using sum-of-squares decomposition

Author

Dumitrescu, Bogdan

Author_Institution

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

Volume

3

fYear

2004

fDate

23-26 May 2004

Abstract

A new stability test for d-dimensional systems is presented. It consists of maximizing the minimum eigenvalue of a positive definite Gram matrix associated with a polynomial positive on the unit d-circle. This formulation is based on expressing the polynomial as a sum of squares and leads to a semidefinite programming (SDP) problem, which can be solved reliably. Although the test is based on a sufficient condition, the practical results are very good. Also, the test has the advantage of not giving false positives.

Keywords

discrete time systems; eigenvalues and eigenfunctions; matrix decomposition; multidimensional systems; polynomials; stability; d-dimensional system; minimum eigenvalue maximization; multidimensional stability test; polynomial positive; positive definite Gram matrix; semidefinite programming problem; sum-of-squares decomposition; unit d-circle; Eigenvalues and eigenfunctions; Equations; Matrix decomposition; Multidimensional signal processing; Multidimensional systems; Polynomials; Stability; Sufficient conditions; System testing; Transfer functions;

fLanguage

English

Publisher

ieee

Conference_Titel

Circuits and Systems, 2004. ISCAS '04. Proceedings of the 2004 International Symposium on

Print_ISBN

0-7803-8251-X

Type

conf

DOI

10.1109/ISCAS.2004.1328804

Filename

1328804