Abstract
In this paper a double integrator system with delayed input controlled by a sub-optimal second order sliding mode control law is considered. The case when the system is affected by a bounded, uncertain dissipative drift term is investigated. It is proven that, due to the input delay, the limit system trajectories are periodic. Moreover it is shown that the amplitude of the limit cycle is reduced by the presence of the disturbance. These results are exploited to synthesize a new control law which guarantees the simultaneous reduction of the amplitude of the oscillations and the reaching time of any neighbourhood of the limit cycle.