Extended Observer Forms for Submersive Discrete-time Systems

Ashutosh Simha; Vadim Kaparin; Tanel Mullari; Ulle Kotta

doi:10.1109/TAC.2023.3336253

Extended Observer Forms for Submersive Discrete-time Systems

Ashutosh Simha, Vadim Kaparin, Tanel Mullari, Ulle Kotta

Networked Systems

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Abstract

—This technical note addresses the problem of transforming a single-input–single-output discrete-time system into the extended observer form, which comprise a linear time-invariant observable component, and a nonlinear injection term, which depends on the input, output, and their forward shifts up to a finite order. Intrinsic necessary and sufficient conditions are provided for obtaining the extended observer form via a parametrized state transformation. The conditions are formulated directly in terms of the state equations and do not rely on input–output equations as in the earlier papers. Further, an algorithm for obtaining the required transformation is presented. Unlike the existing results on observer forms, the results are not restricted to reversible systems but to more general submersive systems, i.e., to systems, which are reversible via static state feedback.

Original language	English
Pages (from-to)	2684-2688
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	69
Issue number	4
DOIs	https://doi.org/10.1109/TAC.2023.3336253
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

Discrete-time system
Discrete-time systems
extended observer form
geometric methods
Manifolds
Nonlinear dynamical systems
nonlinear observers
Observers
Output feedback
Standards
Transforms

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abstract = "—This technical note addresses the problem of transforming a single-input–single-output discrete-time system into the extended observer form, which comprise a linear time-invariant observable component, and a nonlinear injection term, which depends on the input, output, and their forward shifts up to a finite order. Intrinsic necessary and sufficient conditions are provided for obtaining the extended observer form via a parametrized state transformation. The conditions are formulated directly in terms of the state equations and do not rely on input–output equations as in the earlier papers. Further, an algorithm for obtaining the required transformation is presented. Unlike the existing results on observer forms, the results are not restricted to reversible systems but to more general submersive systems, i.e., to systems, which are reversible via static state feedback.",

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AU - Kaparin, Vadim

AU - Mullari, Tanel

AU - Kotta, Ulle

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N2 - —This technical note addresses the problem of transforming a single-input–single-output discrete-time system into the extended observer form, which comprise a linear time-invariant observable component, and a nonlinear injection term, which depends on the input, output, and their forward shifts up to a finite order. Intrinsic necessary and sufficient conditions are provided for obtaining the extended observer form via a parametrized state transformation. The conditions are formulated directly in terms of the state equations and do not rely on input–output equations as in the earlier papers. Further, an algorithm for obtaining the required transformation is presented. Unlike the existing results on observer forms, the results are not restricted to reversible systems but to more general submersive systems, i.e., to systems, which are reversible via static state feedback.

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KW - Observers

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Extended Observer Forms for Submersive Discrete-time Systems

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