Discrete sliding-mode-based differentiators

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

doi:10.1109/VSS.2016.7506910

Discrete sliding-mode-based differentiators

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

School of Mathematical Sciences

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

7 Scopus citations

Abstract

Sliding-mode-based differentiators of the input (t) of the order k yield exact estimations of the derivatives ,..., ^(k), provided an upper bound of |^(k+1)(t)| is available in real-time. Practical application involves discrete noisy sampling of and numeric integration of the internal variables between the measurements. The corresponding asymptotic differentiation accuracies are calculated in the presence of Euler integration and discrete sampling, whereas both independently feature variable or constant time steps. Proposed discrete differentiators restore the optimal accuracy of their continuous-time counterparts. Simulation confirms the presented results.

Original language	English
Title of host publication	2016 14th International Workshop on Variable Structure Systems, VSS 2016
Publisher	IEEE Computer Society
Pages	166-171
Number of pages	6
ISBN (Electronic)	9781467397889
DOIs	https://doi.org/10.1109/VSS.2016.7506910
State	Published - 7 Jul 2016
Event	14th International Workshop on Variable Structure Systems, VSS 2016 - Nanjing, China Duration: 1 Jun 2016 → 4 Jun 2016

Publication series

Name	Proceedings of IEEE International Workshop on Variable Structure Systems
Volume	2016-July
ISSN (Print)	2165-4816
ISSN (Electronic)	2165-4824

Conference

Conference	14th International Workshop on Variable Structure Systems, VSS 2016
Country/Territory	China
City	Nanjing
Period	1/06/16 → 4/06/16

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10.1109/VSS.2016.7506910

Cite this

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title = "Discrete sliding-mode-based differentiators",

abstract = "Sliding-mode-based differentiators of the input (t) of the order k yield exact estimations of the derivatives ,..., (k), provided an upper bound of |(k+1)(t)| is available in real-time. Practical application involves discrete noisy sampling of and numeric integration of the internal variables between the measurements. The corresponding asymptotic differentiation accuracies are calculated in the presence of Euler integration and discrete sampling, whereas both independently feature variable or constant time steps. Proposed discrete differentiators restore the optimal accuracy of their continuous-time counterparts. Simulation confirms the presented results.",

author = "Barbot, {Jean Pierre} and Arie Levant and Miki Livne and Davin Lunz",

note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 14th International Workshop on Variable Structure Systems, VSS 2016 ; Conference date: 01-06-2016 Through 04-06-2016",

year = "2016",

month = jul,

day = "7",

doi = "10.1109/VSS.2016.7506910",

language = "אנגלית",

series = "Proceedings of IEEE International Workshop on Variable Structure Systems",

publisher = "IEEE Computer Society",

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Barbot, JP, Levant, A, Livne, M & Lunz, D 2016, Discrete sliding-mode-based differentiators. in 2016 14th International Workshop on Variable Structure Systems, VSS 2016., 7506910, Proceedings of IEEE International Workshop on Variable Structure Systems, vol. 2016-July, IEEE Computer Society, pp. 166-171, 14th International Workshop on Variable Structure Systems, VSS 2016, Nanjing, China, 1/06/16. https://doi.org/10.1109/VSS.2016.7506910

Discrete sliding-mode-based differentiators. / Barbot, Jean Pierre; Levant, Arie; Livne, Miki et al.
2016 14th International Workshop on Variable Structure Systems, VSS 2016. IEEE Computer Society, 2016. p. 166-171 7506910 (Proceedings of IEEE International Workshop on Variable Structure Systems; Vol. 2016-July).

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

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AB - Sliding-mode-based differentiators of the input (t) of the order k yield exact estimations of the derivatives ,..., (k), provided an upper bound of |(k+1)(t)| is available in real-time. Practical application involves discrete noisy sampling of and numeric integration of the internal variables between the measurements. The corresponding asymptotic differentiation accuracies are calculated in the presence of Euler integration and discrete sampling, whereas both independently feature variable or constant time steps. Proposed discrete differentiators restore the optimal accuracy of their continuous-time counterparts. Simulation confirms the presented results.

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Discrete sliding-mode-based differentiators

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