Estimation of the domain of attraction for polynomial systems

Author

Fan, Youping ; Tibken, Bernd

Author_Institution

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

fYear

2005

fDate

10-13 July 2005

Firstpage

77

Lastpage

82

Abstract

In this paper the asymptotic stability of polynomial nonlinear systems is investigated. Our goal is, based upon modern results of real algebraic geometry, to compute subsets of the region of attraction of asymptotically stable stationary points of polynomial systems. A theorem of Toeplitz and the Lyapunov stability theory are applied to achieve the aim. Especially the inequality conditions given by the theorem of Toeplitz enable the calculation of the inner approximation to the relevant region of the domain of attraction. An instructive example is discussed to show the results of the presented approach.

Keywords

Lyapunov methods; approximation theory; asymptotic stability; geometry; nonlinear systems; polynomials; Lyapunov stability theory; Toeplitz theorem; asymptotic stability; domain of attraction estimation; inner approximation; polynomial nonlinear systems; real algebraic geometry; Asymptotic stability; Differential equations; Eigenvalues and eigenfunctions; Geometry; Linear matrix inequalities; Lyapunov method; Modems; Nonlinear systems; Polynomials; State-space methods;

fLanguage

English

Publisher

ieee

Conference_Titel

Multidimensional Systems, 2005. NDS 2005. The Fourth International Workshop on

Print_ISBN

3-9810299-8-4

Type

conf

DOI

10.1109/NDS.2005.195334

Filename

1507836