Li, Chunji; Ryoo, Cheon Seoung; Li, Ning; Cao, Lili Estimating the domain of attraction via moment matrices. (English) Zbl 1191.34070 Bull. Korean Math. Soc. 46, No. 6, 1237-1248 (2009). 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. Reviewer: Vladimir Răsvan (Craiova) Cited in 6 Documents MSC: 34D45 Attractors of solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations Keywords:domain of attraction; moment matrices; Liapunov function Software:YALMIP PDFBibTeX XMLCite \textit{C. Li} et al., Bull. Korean Math. Soc. 46, No. 6, 1237--1248 (2009; Zbl 1191.34070) Full Text: DOI