×

Estimating the domain of attraction via moment matrices. (English) Zbl 1191.34070

The paper starts from the general system
\[ \dot{x} = f(x) ,\quad x\in \mathbb R^n ,\quad f(0)=0 \]
and looks for the domain of attraction of \(x=0\) estimated by inequalities of the form \(V(x)<c\) where \(V(x)\) is a Liapunov function. To maximize this estimate the following optimization problem is considered
\[ f\text{ind}\;c_* = \min V(x) \]
subject to the constraints \(x\neq 0\), \(W(x)=0\), where
\[ W(x) = \text{grad}_x V(x)\cdot f(x). \]
The paper deals with this problem for the case when the components of \(f:\mathbb R^n\to \mathbb R^n\) are polynomials in \(n\) variables and \(V\) is quadratic, by using the moment matrices for polynomials.

MSC:

34D45 Attractors of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations

Software:

YALMIP
PDFBibTeX XMLCite
Full Text: DOI