Guaranteeing Disturbance Rejection and Control Signal Continuity for the Saturated Super-Twisting Algorithm

The saturated super-twisting algorithm is a second order sliding-mode control law for robust control in the presence of a bounded control input. Its implementation is based on a switching logic and the resulting control signal typically exhibits a single jump discontinuity. This contribution presents novel stability conditions that allow for tuning the algorithm such that perturbation amplitudes up to the control input bound are rejected with a continuous control signal. A simplified control law is furthermore proposed, which is equivalent to the original algorithm while being easier to implement.