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.
Original language | English |
---|---|
Article number | 110983 |
Number of pages | 5 |
Journal | Automatica |
Volume | 152 |
DOIs | |
Publication status | Published - 2023 |
Keywords
- robust exact differentiator
- super-twisting algorithm
- differentiation error
- accuracy
- Lyapunov function
- Accuracy
- Differentiation error
- Robust exact differentiator
- Super-twisting algorithm
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Control and Systems Engineering