Worst-case error bounds for the super-twisting differentiator in presence of measurement noise

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...

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Bibliographic Details
Published in:Automatica (Oxford) 2023-06, Vol.152, p.110983, Article 110983
Main Author: Seeber, Richard
Format: Article
Language:English
Subjects:
Accuracy
Differentiation error
Lyapunov function
Robust exact differentiator
Super-twisting algorithm
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2023.110983