Discrete-Time Implementation of Homogeneous Differentiators

Research output: Contribution to journalArticleResearchpeer-review

Abstract

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 w.r.t.
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.
LanguageEnglish
JournalIEEE Transactions on Automatic Control
DOIs
StatusE-pub ahead of print - 2019

Fingerprint

Sampling
Derivatives

Cite this

Discrete-Time Implementation of Homogeneous Differentiators. / Koch, Stefan; Reichhartinger, Markus; Horn, Martin; Fridman, Leonid.

In: IEEE Transactions on Automatic Control, 2019.

Research output: Contribution to journalArticleResearchpeer-review

@article{089929cd14c24d49b1db9d2bda55320a,
title = "Discrete-Time Implementation of Homogeneous Differentiators",
abstract = "The discrete-time version of Levant's arbitrary order robust exactdifferentiator, which is a forward Euler discretized version of thecontinuous-time algorithm enhanced by linear higher-order terms, isextended by taking into account also nonlinear higher-order terms. Theresulting differentiator preserves the asymptotic accuracies w.r.t.sampling and noise known from the continuous-time algorithm. It isdemonstrated in a simulation example and by differentiating a measuredsignal that the nonlinear higher-order terms allow reducing the highfrequency switching amplitude whenever the (n+1)th derivative of thesignal to be differentiated vanishes, leading to an improvement in theprecision.",
author = "Stefan Koch and Markus Reichhartinger and Martin Horn and Leonid Fridman",
year = "2019",
doi = "10.1109/TAC.2019.2919237",
language = "English",
journal = "IEEE Transactions on Automatic Control",
issn = "0018-9286",
publisher = "IEEE Control Systems Society",

}

TY - JOUR

T1 - Discrete-Time Implementation of Homogeneous Differentiators

AU - Koch, Stefan

AU - Reichhartinger, Markus

AU - Horn, Martin

AU - Fridman, Leonid

PY - 2019

Y1 - 2019

N2 - The discrete-time version of Levant's arbitrary order robust exactdifferentiator, which is a forward Euler discretized version of thecontinuous-time algorithm enhanced by linear higher-order terms, isextended by taking into account also nonlinear higher-order terms. Theresulting differentiator preserves the asymptotic accuracies w.r.t.sampling and noise known from the continuous-time algorithm. It isdemonstrated in a simulation example and by differentiating a measuredsignal that the nonlinear higher-order terms allow reducing the highfrequency switching amplitude whenever the (n+1)th derivative of thesignal to be differentiated vanishes, leading to an improvement in theprecision.

AB - The discrete-time version of Levant's arbitrary order robust exactdifferentiator, which is a forward Euler discretized version of thecontinuous-time algorithm enhanced by linear higher-order terms, isextended by taking into account also nonlinear higher-order terms. Theresulting differentiator preserves the asymptotic accuracies w.r.t.sampling and noise known from the continuous-time algorithm. It isdemonstrated in a simulation example and by differentiating a measuredsignal that the nonlinear higher-order terms allow reducing the highfrequency switching amplitude whenever the (n+1)th derivative of thesignal to be differentiated vanishes, leading to an improvement in theprecision.

U2 - 10.1109/TAC.2019.2919237

DO - 10.1109/TAC.2019.2919237

M3 - Article

JO - IEEE Transactions on Automatic Control

T2 - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

ER -