Attractor estimates for an energy-controlled pendulum in presence of irregular bounded disturbance ?

摘要

The problem of pendulum’s energy control in presence of an irregular input disturbance is considered. A feedback control law is chosen based on the speed gradient method. The main contribution of the paper is in studying the complex behavior of the previously designed system under irregular disturbances. The main result is precise estimates for an initial set and a limit set (attractor) as well as the conditions guaranteeing the following: all the solutions starting in the initial set will enter the limit set in a finite time.