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Methods for determination and approximation of the domain of attraction. (English) Zbl 1066.34053
Consider the initial value problem $\frac{dx}{dt} =f(x) , x(0)=x^0$, where $f\in C^1(\Bbb R^n,\Bbb R^n)$ with $f(0)=0$. Assume that $x=0$ is asymptotically stable and $D_{a}(0)$ denotes the domain of attraction of 0. The authors introduce several approaches for the determination of $D_{a}(0)$. In order to determine and approximate $D_{a}(0)$ for an $R$-analytical system, an $R$-analytical function and the sequence of its Taylor polynomials are constructed by recurrence formula using the coefficients of the power series expansion of $f$ at 0. This construction differs from that one of {\it A. Vannelli} and {\it M. Vidyasagar} [Automatica 21, 69--80 (1985; Zbl 0559.34052)].

MSC:
 34D20 Stability of ODE
Full Text:
References:
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