Super-Twisting algorithm for systems with uncertain control gain: A Lyapunov based approach

A Lyapunov based analysis of convergence for the Super-Twisting algorithm for systems with uncertain control gain is presented. Through a Lyapunov function we have found the conditions over the matched perturbations and the uncertain control gain to preserve the properties of insensitivity and finite-time convergence to Sliding Modes of order two, that the Super-Twisting algorithm is able to achieve.