LMI Tests for Positive Definite Polynomials: Slack Variable Approach

Author

Peaucelle, Dimitri ; Sato, Masayuki

Author_Institution

LAAS-CNRS, Univ. de Toulouse, Toulouse

Volume

54

Issue

4

fYear

2009

fDate

4/1/2009 12:00:00 AM

Firstpage

886

Lastpage

891

Abstract

The considered problem is assessing non-negativity of a function´s values when indeterminates are in domains constrained by scalar polynomial inequalities. The tested functions are multi-indeterminates polynomial matrices which are required to be positive semi-definite. New tests based on linear matrix inequalities are provided in a Slack Variables type approach. The results are compared to those obtained via the Sum-Of-Squares approach. They are proved to be equivalent in case of unbounded domains and less conservative if polytopic-type bounds are known.

Keywords

linear matrix inequalities; polynomials; linear matrix inequalities; multiindeterminates polynomial matrices; positive definite polynomials; scalar polynomial inequalities; slack variable approach; sum-of-squares approach; Educational technology; Linear matrix inequalities; Matrix decomposition; Nonlinear systems; Performance analysis; Polynomials; Programming profession; Robust stability; Robustness; Space technology; Testing; Linear matrix inequality (LMI); matrix-valued polynomials; positivity; robustness; sum-of-squares;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2008.2010971

Filename

4806156