—The differentiators based on the Super-Twisting Algorithm (STA) yield finite-time and theoretically exact convergence to the derivative of the input signal, whenever this derivative is Lipschitz. However, the convergence time grows unboundedly when the initial conditions of the differentiation error grow. In this paper a Uniform Robust Exact Differentiator… (More)
—A method to compute the differentiation error in presence of bounded measurement noise for the family of Generalized Super-Twisting differentiators is presented. The proposed method allows choosing the optimal gain of each differentiator in the family providing the smallest ultimate bound of the differentiation error. In particular, an heuristic formula… (More)
—In this paper a novel, Lyapunov-based, variable-gain super-twisting algorithm is proposed. It ensures for linear time invariant systems the global, finite-time convergence to the desired sliding surface, when the matched perturbations/uncertainties are Lipschitz-continuous functions of time, that are bounded, together with their derivatives, by known… (More)
— In this paper we obtain a homogeneous, continuous , quadratic and strict Lyapunov function for Levant's Second Order Differentiator. Since its derivative is a non quadratic, discontinuous, homogeneous form its negative definiteness is determined using some new inequalities, providing coarser bounds than Young's inequalities.