Contribuições para o problema de estabilização de sistemas não lineares usando Teoria da Dissipatividade

Abstract

This dissertation deals with the topic of stabilization of nonlinear systems through iterative methods to design a SOF controller using concepts of Lyapunov theory and dissipativity. Although the methods are available in the literature, there has not yet been a comparative study, exploring the potential of each method or the benefits of their respective uses. Through these studies, it is possible to obtain guidance to develop more optimized versions. The objective of this work is to contribute to the problem of stabilization of nonlinear systems using dissipativity theory, analyzing and comparing methods from the literature and presenting new conditions, allowing the expansion of methods to cover more classes of nonlinear non-affine systems at the input and the stabilization of nonlinear systems using rational Lyapunov functions. Then, the methods are subjected to numerical examples to validate the performance of each approach. The analysis is performed using convergence time, number of iterations and number of calculated variables. The comparison makes it clear that one method stands out among the others and that it was possible to use the new conditions proposed to stabilize this class of nonlinear systems. It is also possible to conclude that the estimation of the attraction domain using rational Lyapunov functions is much better when compared to the polynomial case.