On a method of evaluation of attraction domain for fixed point of nonlinear point mapping of arbitrary dimension

In this paper we describe the method of attraction domain evaluation for equilibrium states of nonlinear discrete dynamic system based on Lyapunov functions method. Attraction domain evaluation size is equilibrium state neighborhood where the first difference of Lyapunov function is negative. Lyapunov function is chosen as positive quadratic form for which the negativity of its first difference by virtue of linearized system is guaranteed with given supply. We propose the method of attraction domain extension.