Discrete differentiators based on sliding modes

Jean Pierre Barbot, Arie Levant, Miki Livne, Davin Lunz

Research output: Contribution to journalArticlepeer-review


Sliding-mode-based differentiation of the input f(t) yields exact estimations of the derivatives ḟ,…,f(n), provided an upper bound L(t) of |f(n+1)(t)| is available in real-time. In practice it involves discrete sampling and numerical integration of the internal variables between the measurements. Accuracy asymptotics of different discretization schemes are calculated for discrete noisy sampling, whereas sampling and integration steps are independently variable or constant. Proposed discrete differentiators restore the optimal accuracy asymptotics of their continuous-time counterparts. Event-triggered sampling is considered. Extensive numeric experiments are presented and analyzed.

Original languageEnglish
Article number108633
StatePublished - Feb 2020


  • Accuracy
  • Differentiators
  • Digital filters
  • Sampled signals
  • Sliding mode


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