Finite-time convergence analysis for “Twisting” controller via a strict Lyapunov function

Abstract

A second order sliding mode controller, the so- called “Twisting” algorithm is under study. A non-smooth strict Lyapunov function is proposed, such that global finite time stability for this algorithm can be proved even in the case when it is affected by bounded external perturbations. The strict Lyapunov function gives the possibility to estimate an upper bound for the time convergence of the trajectories of the system to the equilibrium point. A linear compensator is added to the twisting algorithm so linearly increasing perturbations can be compensated. Indeed, finite time stability and a convergence time estimation for a global finite time convergence algorithm is shown.