Robust Exact Differentiator inspired Discrete-Time Differentiation

Maximilian Rüdiger-Wetzlinger; Markus Reichhartinger; Martin Horn

doi:10.1109/TAC.2021.3093522

Robust Exact Differentiator inspired Discrete-Time Differentiation

Maximilian Rüdiger-Wetzlinger^*, Markus Reichhartinger, Martin Horn

^*Corresponding author for this work

Institute of Automation and Control (4430)

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Journal	IEEE Transactions on Automatic Control
DOIs	https://doi.org/10.1109/TAC.2021.3093522
Publication status	E-pub ahead of print - 2021

Keywords

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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10.1109/TAC.2021.3093522

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title = "Robust Exact Differentiator inspired Discrete-Time Differentiation",

abstract = "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",

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

author = "Maximilian R{\"u}diger-Wetzlinger and Markus Reichhartinger and Martin Horn",

year = "2021",

doi = "10.1109/TAC.2021.3093522",

language = "English",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "IEEE Control Systems Society",

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TY - JOUR

T1 - Robust Exact Differentiator inspired Discrete-Time Differentiation

AU - Rüdiger-Wetzlinger, Maximilian

AU - Reichhartinger, Markus

AU - Horn, Martin

PY - 2021

Y1 - 2021

N2 - 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

AB - 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

KW - Asymptotic stability

KW - Convergence

KW - Discrete-time systems

KW - Eigenvalues and eigenfunctions

KW - Heuristic algorithms

KW - Perturbation methods

KW - Sliding mode control

KW - Stability criteria

KW - Stability of nonlinear systems

KW - Tuning

UR - http://www.scopus.com/inward/record.url?scp=85112209348&partnerID=8YFLogxK

U2 - 10.1109/TAC.2021.3093522

DO - 10.1109/TAC.2021.3093522

M3 - Article

SN - 0018-9286

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

ER -

Robust Exact Differentiator inspired Discrete-Time Differentiation

Abstract

Keywords

ASJC Scopus subject areas

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