Worst-case error bounds for the super-twisting differentiator in presence of measurement noise. (June 2023)

• Record Type: Journal Article
• Authors: Seeber, Richard
• Is Part Of: Automatica. Volume 152(2023)
• Publication Date: 2023-06
• Subjects: Robust exact differentiator -- Super-twisting algorithm -- Differentiation error -- Accuracy -- Lyapunov function; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2023.110983
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The super-twisting differentiator, also known as the first-order robust exact differentiator, is a well known sliding mode differentiator. In the absence of measurement noise, it achieves exact reconstruction of the time derivative of a function with bounded second derivative. This note proposes an upper bound for its worst-case differentiation error in the presence of bounded measurement noise, based on a novel Lipschitz continuous Lyapunov function. It is shown that the bound can be made arbitrarily tight and never exceeds the true worst-case differentiation error by more than a factor of two. A numerical simulation illustrates the results and also demonstrates the non-conservativeness of the proposed bound.