A class of multilinear uncertain polynomials to which the edge theorem is applicable

Author

Chen, Weining ; Petersen, Ian R.

Author_Institution

JRCASE, Macquarie Univ., North Ryde, NSW, Australia

Volume

40

Issue

12

fYear

1995

fDate

12/1/1995 12:00:00 AM

Firstpage

2103

Lastpage

2107

Abstract

This paper gives a class of multilinear uncertain polynomials to which the edge theorem is applicable. In the paper, a notion of “symmetric uncertainty structure” is introduced. The main result is as follows: if a multilinear uncertain polynomial has a symmetric uncertainty structure and the uncertain parameters are nonoverlapping, then the corresponding value sets will be convex polygons. This means that the use of the zero exclusion condition to test the robust stability of such uncertain polynomials is feasible since we need only to calculate the extreme points of the convex polygons. Furthermore, a version of the edge theorem can be used to test the robust stability of such uncertain polynomials

Keywords

polynomials; robust control; set theory; uncertain systems; convex polygons; edge theorem; multilinear uncertain polynomials; robust stability; symmetric uncertainty structure; uncertain parameters; uncertain polynomials; zero exclusion condition; Australia Council; Control systems; Polynomials; Robust control; Robust stability; Robustness; Sufficient conditions; Testing; Uncertainty;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.478333

Filename

478333