Estudo de sistemas dinâmicos com atraso variante no tempo

Abstract

This undergraduate thesis presents analysis and simulations of dynamical systems with time-varying delay. The simulations are presented after a review of the basic theory of Lyapunov stability of dynamical systems as well as a brief explanation about the effects of constant time delay on linear and time-invariant systems. A relationship between sampled data control systems and delay differential systems with time-varying delay is detailed, followed by a description of the the effects associated to the quenching phenomenon and a an exposition of the ideas related to the numerical methods used for obtaining delayed differential equations solutions. Additionally, the behaviors of first and second order PI-controlled systems with constant delay are compared with respect to the case in which those systems have a time-varying delay.