Linear matrix inequalities for robust strictly positive real design

Author

Henrion, Didier

Author_Institution

Lab. d´´Analyse et d´´Archit. des Systemes, Centre Nat. de la Recherche Scientifique, Toulouse, France

Volume

49

Issue

7

fYear

2002

fDate

7/1/2002 12:00:00 AM

Firstpage

1017

Lastpage

1020

Abstract

A necessary and sufficient condition is proposed for the existence of a polynomial p(s) such that the rational function p(s)/q(s) is robustly strictly positive real when q(s) is a given Hurwitz polynomial with polytopic uncertainty. It turns out that the whole set of candidates p(s) is a convex subset of the cone of positive semidefinite matrices, resulting in a straightforward strictly positive real design algorithm based on linear matrix inequalities

Keywords

continuous time systems; mathematical programming; matrix algebra; polynomials; rational functions; stability; uncertain systems; Hurwitz polynomial; continuous-time case; linear matrix inequalities; necessary sufficient condition; polynomial existence; polytopic uncertainty; positive semidefinite matrices; rational function; robust strictly positive real design; semidefinite programming; strictly positive real design algorithm; uncertain systems; Algorithm design and analysis; Asymptotic stability; Control systems; Linear matrix inequalities; Polynomials; Robustness; Sufficient conditions; Transfer functions; Uncertain systems; Uncertainty;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/TCSI.2002.800838

Filename

1016836