Methods for determination and approximation of the domain of attraction

In this paper, an R-analytical function and the sequence of its Taylor polynomials (which are Lyapunov functions different from those of Vanelli and Vidyasagar (Automatica 21(1) (1985) 69-80)) is presented, in order to determine and approximate the domain of attraction of the exponentially asymptotically stable zero steady state of an autonomous, R-analytical system of differential equations. The analytical function and the sequence of its Taylor polynomials are constructed by recurrence formulae using the coefficients of the power series expansion of f at 0.