Robust time-sub-optimal control of the saturated double integrator applied to attitude stabilization

This paper proposes a robust time-sub-optimal controller for the double integrator with saturated input, based on a hybrid blend of a local and a global controller. The scheme makes use of two hysteresis mechanisms in order to provide robustness to unmodelled dynamics and measurement noise. Rigorous certificates of the stability of the proposed controller are given, by exploiting the properties of hybrid dynamical system established in recent works of Teel et al. Attitude stabilization with the proposed control strategy is then illustrated by simulations. The method shows its effectiveness in stabilizing the attitude, preventing the typical chattering and robustness issues emerging with classical time-optimal implementations.