English title

Lyapunov method is an effective method to prove the stability of the equilibrium points of dynamical systems. One of the applications of the Lyapunov analysis, is estimation of the region of attraction. In general, based on the selected Lyapunov function, a portion of the region of attraction is estimated that may not be the best. In this paper, via proposing an algorithm for generating Lyapunov candidate functions in a series from, a method is developed by which, in each step ahead, a modified estimation of the region of attraction is presented. The main idea of generation of the mentioned entries, is constructing a new Lyapunov function using a linear combination of the current Lyapunov function with its derivative. According to each candidate Lyapunov function, a region of attraction is constructed so that in the generation process of the new functions, every estimated region of attraction is subset of the next estimation. Finally, to show the effectiveness of the obtained results, some numerical examples are simulated.