Abstract
This paper investigates the problem of estimating an asymptotic stability region of nonlinear polynomial discrete-time systems. To achieve an appropriate estimation of subsets of attraction regions for asymptotically stable equilibrium points, the reverse trajectory formalism is applied through the formulation of iterative algorithms. The developed methods enable us to obtain enlarged circular domains of attraction that are comparable with the ones obtained by delicate computational procedures. The main advantage of the synthesized algorithms is that they disregard the problem of constructing Lyapunov function to achieve the control target for nonlinear systems. An instructive example of a power electrical system is used as an illustration of the results of the synthesized approaches.