Optimal gain for the Super-Twisting differentiator in the presence of measurement noise

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 for the optimal gain of the pure Super-Twisting differentiator is presented. A numerical analysis comparing the performance of linear High-Gain and Super-Twisting differentiators is presented.