Homogeneous discrete differentiation of functions with unbounded higher derivatives

Miki Livne; Arie Levant

doi:https://doi.org/10.1109/CDC.2013.6760137

Homogeneous discrete differentiation of functions with unbounded higher derivatives

Miki Livne, Arie Levant

School of Mathematical Sciences

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Homogeneous sliding-mode-based differentiators (HD) are known for their high asymptotic accuracy. Their practical realization is computer-based and requires discretization. The corresponding combination of a discrete system with a continuous-time input signal produces hybrid dynamics. In the case of the most usual one-step Euler discretization that hybrid system lacks the homogeneity of its predecessor and loses its ultimate accuracy. Nevertheless, the discrete differentiator can be modified, restoring the homogeneity and the accuracy of HD. Similarly to HD, the proposed homogeneous discrete differentiator can also be used to differentiate signals with a variable upper bound of the highest derivative. Simulation results confirm the theoretical results.

Original language	English
Title of host publication	2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1762-1767
Number of pages	6
ISBN (Print)	9781467357173
DOIs	https://doi.org/10.1109/CDC.2013.6760137
State	Published - 2013
Event	52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy Duration: 10 Dec 2013 → 13 Dec 2013

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control

Conference

Conference	52nd IEEE Conference on Decision and Control, CDC 2013
Country/Territory	Italy
City	Florence
Period	10/12/13 → 13/12/13

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modelling and Simulation
Control and Optimization

Access to Document

https://doi.org/10.1109/CDC.2013.6760137

Cite this

Livne, M., & Levant, A. (2013). Homogeneous discrete differentiation of functions with unbounded higher derivatives. In 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013 (pp. 1762-1767). Article 6760137 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760137

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title = "Homogeneous discrete differentiation of functions with unbounded higher derivatives",

abstract = "Homogeneous sliding-mode-based differentiators (HD) are known for their high asymptotic accuracy. Their practical realization is computer-based and requires discretization. The corresponding combination of a discrete system with a continuous-time input signal produces hybrid dynamics. In the case of the most usual one-step Euler discretization that hybrid system lacks the homogeneity of its predecessor and loses its ultimate accuracy. Nevertheless, the discrete differentiator can be modified, restoring the homogeneity and the accuracy of HD. Similarly to HD, the proposed homogeneous discrete differentiator can also be used to differentiate signals with a variable upper bound of the highest derivative. Simulation results confirm the theoretical results.",

author = "Miki Livne and Arie Levant",

year = "2013",

doi = "https://doi.org/10.1109/CDC.2013.6760137",

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pages = "1762--1767",

booktitle = "2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013",

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note = "52nd IEEE Conference on Decision and Control, CDC 2013 ; Conference date: 10-12-2013 Through 13-12-2013",

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Livne, M & Levant, A 2013, Homogeneous discrete differentiation of functions with unbounded higher derivatives. in 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013., 6760137, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 1762-1767, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 10/12/13. https://doi.org/10.1109/CDC.2013.6760137

Homogeneous discrete differentiation of functions with unbounded higher derivatives. / Livne, Miki; Levant, Arie.
2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013. Institute of Electrical and Electronics Engineers Inc., 2013. p. 1762-1767 6760137 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Homogeneous sliding-mode-based differentiators (HD) are known for their high asymptotic accuracy. Their practical realization is computer-based and requires discretization. The corresponding combination of a discrete system with a continuous-time input signal produces hybrid dynamics. In the case of the most usual one-step Euler discretization that hybrid system lacks the homogeneity of its predecessor and loses its ultimate accuracy. Nevertheless, the discrete differentiator can be modified, restoring the homogeneity and the accuracy of HD. Similarly to HD, the proposed homogeneous discrete differentiator can also be used to differentiate signals with a variable upper bound of the highest derivative. Simulation results confirm the theoretical results.

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PB - Institute of Electrical and Electronics Engineers Inc.

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Homogeneous discrete differentiation of functions with unbounded higher derivatives

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All Science Journal Classification (ASJC) codes

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