Abstract
A double integrator with delayed input is considered. We prove that the system, when controlled by a sub-optimal second order feedback law, shows, in the limit, a periodic behaviour. The trajectories in the phase plane converge to a limit cycle. Then, by exploiting the results established in the first part of the paper, we introduce a new control law that guarantees a step by step reduction of the size of the limit cycle. Therefore the asymptotic stability of the closed loop system is ensured.