Optimal Lyapunov function selection for reaching time estimation of Super Twisting algorithm

In this paper we propose a whole family of quadratic-like strong Lyapunov functions for the Super Twisting algorithm. They show that all trajectories converge in finite time to the origin, and a formula to estimate the convergence time for the considered family of Lyapunov functions is proposed. A methodology to select the Lyapunov function, providing for better estimation of the convergence time, is presented. The obtained results are illustrated through simulation.