Robust Exact Differentiator inspired Discrete-Time Differentiation

Maximilian Rüdiger-Wetzlinger*, Markus Reichhartinger, Martin Horn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper proposes a discrete-time differentiation algorithm of arbitrary order inspired by the continuous-time uniform robust exact differentiator and the continuous-time arbitrary order robust exact differentiator. As the well-known explicit Euler method is not suitable for discretizing algorithms with the fixed-time convergence property, a semi-implicit approach is proposed. The discrete-time differentiators of order 2 and 3 are studied in detail and it is proven that the estimation errors vanish independent of their initial condition in the unperturbed case. In the presence of perturbations it is shown that the origin of the estimation errors is surrounded by an attractive invariant set. Furthermore the performance of the proposed algorithm is evaluated via simulation studies
Original languageEnglish
JournalIEEE Transactions on Automatic Control
Publication statusE-pub ahead of print - 2021


  • Asymptotic stability
  • Convergence
  • Discrete-time systems
  • Eigenvalues and eigenfunctions
  • Heuristic algorithms
  • Perturbation methods
  • Sliding mode control
  • Stability criteria
  • Stability of nonlinear systems
  • Tuning

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Computer Science Applications


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