Second order sliding mode control of a perturbed double integrator with state constraints

This paper introduces a second order sliding mode controller for double integrators subject to external disturbances and model uncertainties, with both control and state constraints. The proposed control strategy proves to be able to robustly steer the system state to zero in a finite time, fulfilling the state constraints in spite of the uncertainties, provided that the initial state is inside a given region. The effectiveness of the proposal is then tested on a simulation example.