Estimation of the domain of attraction for polynomial systems using multidimensional grids

Author

Tibken, B. ; Hachicho, O.

Author_Institution

Fac. of Electr. & Inf. Eng., Wuppertal Univ., Germany

Volume

4

fYear

2000

fDate

2000

Firstpage

3870

Abstract

Investigation of the stability properties of stationary points of nonlinear systems lies at the heart of modern control engineering. In this contribution we show how the theorem of Ehlich and Zeller (1964) is used to compute subsets of the domain of attraction of asymptotically stable stationary points of polynomial systems. The theorem of Ehlich and Zeller is a tool to bound the values of a polynomial over an interval using the values of the polynomial on a finite grid in the interval. We present the generalizations of this theorem to multivariable polynomials and to trigonometric polynomials. A bisection strategy is presented which allows the guaranteed computation of a subset of the domain of attraction. An instructive example is presented and some conclusions and an outlook finish the contribution

Keywords

Lyapunov methods; asymptotic stability; differential equations; matrix algebra; nonlinear control systems; optimisation; polynomials; asymptotically stable stationary points; bisection strategy; domain of attraction; multidimensional grids; multivariable polynomials; polynomial systems; stability properties; trigonometric polynomials; Control engineering; Control theory; Heart; Linear matrix inequalities; Lyapunov method; Multidimensional systems; Nonlinear systems; Polynomials; Stability; Symmetric matrices;

fLanguage

English

Publisher

ieee

Conference_Titel

Decision and Control, 2000. Proceedings of the 39th IEEE Conference on

Conference_Location

Sydney, NSW

ISSN

0191-2216

Print_ISBN

0-7803-6638-7

Type

conf

DOI

10.1109/CDC.2000.912316

Filename

912316