Análise de estabilidade utilizando funções de Lyapunov racionais

Abstract

This work addresses the analysis of the stability of nonlinear systems using an iterative method, using concepts from Lyapunov theory and rational functions. Despite the existence of several methods in the literature for analyzing these systems, many of them are iterative and sensitive to initialization, making the analysis of the initialization variable and its impact on the final results crucial. The studies developed here aim to provide direction for refining these methods, enabling more accurate decisions. The central purpose of this work is to contribute to solving the problem of analyzing nonlinear systems, through the application of Lyapunov stability theory, particularly using rational functions. The analysis is conducted by comparing the behavior of a non-affine nonlinear system at the input and an affine nonlinear system. Parameters considered for evaluation include the size of the Attraction Region and the initial Attraction Domain Estimation Function. The comparison highlights the substantial influence of the initialization function on the final results. We further conclude that the attraction domain estimates, when rational Lyapunov functions are employed, significantly outperform those obtained by polynomial approaches.