Robust exact differentiators with predefined convergence time

Richard Seeber*, Hernan Haimovich, Martin Horn, Leonid Fridman, Hernán De Battista

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The problem of exactly differentiating a signal with bounded second derivative is considered. A class of differentiators is proposed, which converge to the derivative of such a signal within a fixed, i.e., a finite and uniformly bounded convergence time. A tuning procedure is derived that allows to assign an arbitrary, predefined upper bound for this convergence time. It is furthermore shown that this bound can be made arbitrarily tight by appropriate tuning. The usefulness of the procedure is demonstrated by applying it to the well-known uniform robust exact differentiator, which is included in the considered class of differentiators as a special case.
Original languageEnglish
Article number109858
Number of pages12
Publication statusPublished - Dec 2021


  • Disturbance rejection
  • Finite-time convergence
  • Fixed-time convergence
  • Sliding modes
  • Super-twisting algorithm

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering

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