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Methods for determination and approximation of the domain of attraction. (English) Zbl 1066.34053

Consider the initial value problem

dx dt=f(x),x(0)=x 0 , where fC 1 ( n , 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 A. Vannelli and M. Vidyasagar [Automatica 21, 69–80 (1985; Zbl 0559.34052)].

MSC:
34D20Stability of ODE