Inducing periodic oscillations and chaos in continuous systems via time-delay controllers

A technique to produce periodic and chaotic oscillations in simple continuous-time systems that without control do not necessarily exhibit an oscillatory behavior, is proposed. First a fast dynamics is produced using a feedback linearization controller such that the closed-loop system can be given a singular perturbation structure. Then a second control term containing a nonlinear map of a delayed state is added. This map produces periodic oscillations and chaos in the sense of Li and Yorke (1975)