Discrete-Time Implementation of Homogeneous Differentiators

Stefan Koch, Markus Reichhartinger*, Martin Horn, Leonid Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The discrete-time version of Levant's arbitrary order robust exact differentiator, which is a forward Euler discretized version of the continuous-time algorithm enhanced by linear higher order terms, is extended by taking into account also nonlinear higher order terms. The resulting differentiator preserves the asymptotic accuracies with respect to sampling and noise known from the continuous-time algorithm. It is demonstrated in a simulation example and by differentiating a measured signal that the nonlinear higher order terms allow reducing the high-frequency switching amplitude whenever the (n+1)th derivative of the signal to be differentiated vanishes, leading to an improvement in the precision.

Original languageEnglish
Article number8723642
Pages (from-to)757-762
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number2
Publication statusPublished - Feb 2019


  • Estimation
  • robust exact differentiator
  • sampled data control
  • sliding-mode control

ASJC Scopus subject areas

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

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