Extended observer form with vector fields

Tanel Mullari; Ülle Kotta; Arvo Kaldmäe; Vadim Kaparin; Ashutosh Simha

doi:10.1080/00207179.2023.2274060

Extended observer form with vector fields

Tanel Mullari^*, Ülle Kotta, Arvo Kaldmäe, Vadim Kaparin, Ashutosh Simha

^*Corresponding author for this work

Networked Systems

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Abstract

This paper addresses the problem of transforming a single-input single-output discrete-time system into the extended observer form which comprises a linear observable component and a nonlinear injection term depending on the input, output and their forward shifts up to a finite order. The necessary and sufficient conditions for the existence of the extended observer form are provided in terms of vector fields. The algorithm is presented to find a parametrised state transformation necessary to transform the system into the extended observer form. The obtained results are applicable also in case of non-reversible systems.

Original language	English
Pages (from-to)	2399-2412
Number of pages	14
Journal	International Journal of Control
Volume	97 (2024)
Issue number	10
DOIs	https://doi.org/10.1080/00207179.2023.2274060
Publication status	Published - 2023

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

algebraic approach
Discrete-time system
extended observer form
nonlinear control system
parametrised state transformation

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10.1080/00207179.2023.2274060

Extended observer form with vector fieldsFinal published version, 1.42 MB

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AU - Kotta, Ülle

AU - Kaldmäe, Arvo

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AU - Simha, Ashutosh

N1 - Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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N2 - This paper addresses the problem of transforming a single-input single-output discrete-time system into the extended observer form which comprises a linear observable component and a nonlinear injection term depending on the input, output and their forward shifts up to a finite order. The necessary and sufficient conditions for the existence of the extended observer form are provided in terms of vector fields. The algorithm is presented to find a parametrised state transformation necessary to transform the system into the extended observer form. The obtained results are applicable also in case of non-reversible systems.

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Extended observer form with vector fields

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