Title :
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
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;
Conference_Titel :
Multidimensional Systems, 2005. NDS 2005. The Fourth International Workshop on
Print_ISBN :
3-9810299-8-4
DOI :
10.1109/NDS.2005.195334
