Estabilização de sistemas de circuito fechado

Abstract

In this work we give an introduction to the theory of stabilization of control systems, focusing on closed-loop systems, with that intent we utilize tools of the theory of differential equations, in particular the theory of the stability of differential equations, and we also use results of linear algebra in the form of theorems about linear control systems as so as classical results of analysis in Rn. The control systems are presented both in euclidean spaces and in smooth manifolds, therefore the theoretical foundation adresses concepts and results of these two ambients, in order to support the final results of the work. The differential equations and their solutions are studied rigorously and the theory of estability of solutions brings the most known methods, such as the Lyapunov method. Because it is an introduction, the emphasis is on the autonomous linear control systems and the results obtained for them are, whenever possible, applied to the most general cases. Many examples are presented throughout the text to assist in understanding the subjects. We also discuss some facts about the Lie theory, adressing Lie groups and Lie algebras and some of the maps that relate them.