Stability conditions for polytopes of polynomials

Author

Rantzer, Anders

Author_Institution

Dept. of Math., R. Inst. of Technol., Stockholm, Sweden

Volume

37

Issue

1

fYear

1992

fDate

1/1/1992 12:00:00 AM

Firstpage

79

Lastpage

89

Abstract

In considering the stability or performance of linear systems with uncertain parameters one is led to consider the simultaneous stability of families of polynomials. For a general stability region in the complex plane, the author gives a stability criterion for polytopes of polynomials in terms of the stability of a minimal number of corners and edges of the polytope. The testing set of edges and corners depends entirely on the edge directions of the polytope; hence the results are particularly applicable to problems with fixed directions, but varying lengths and positions of the edges. Applications to robust pole placement of uncertain systems and computation of worst case H_∞ norms are demonstrated

Keywords

linear systems; optimal control; poles and zeros; polynomials; stability criteria; H_∞ norms; complex plane; edge directions; linear systems; pole placement; polynomials; polytopes; stability criterion; uncertain systems; Linear systems; Mathematics; Polynomials; Robustness; Stability analysis; Stability criteria; State feedback; Testing; Transfer functions; Uncertain systems;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.109640

Filename

109640