Abstract
In this paper the behaviour of a double integrator system with delayed input controlled by a sub-optimal second order sliding mode control law is investigated. Due to the input delay, in the limit the system trajectories are periodic. Whenever the control modulus is chosen to be constant, the amplitude and period of the resulting oscillations are fixed for any initial value. If the control behaves asymmetrically, it is shown that this is no more true, since the overall dynamical system can admit multiple limit cycles.