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Classical observer form for discrete-time nonlinear system: MIMO case.

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Title: Classical observer form for discrete-time nonlinear system: MIMO case.
Alternate Title: Mitme sisendi ja väljundiga diskreetse mittelineaarse juhtimissüsteemi klassikaline vaatlejakuju.
Authors: Kaldmäe, Arvo1, Kaparin, Vadim1, Kotta, Ülle1, Mullari, Tanel2 tanel.mullari@taltech.ee, Tõnso, Maris1
Source: Proceedings of the Estonian Academy of Sciences. 2026, Vol. 75 Issue 1, p2-14. 13p.
Subjects: Discrete-time systems, Coordinate transformations, Dynamical systems, Vector fields, Observability (Control theory), Geometric approach
Abstract (English): The paper addresses the problem of transforming multi-input multi-output discrete-time nonlinear state equations into the classical observer form using state transformation. Necessary and sufficient geometric solvability conditions are given in terms of vector fields. The results obtained generalize the previous ones in several aspects. First, the results are also applicable to non-reversible systems. Second, they hold almost everywhere, not only around the equilibrium point of the system. The generalizations are possible due to the use of different mathematical tools. The proof of sufficiency also provides a method for finding the state transformation. The results are illustrated by two examples. [ABSTRACT FROM AUTHOR]
Abstract (Estonian): Artikkel käsitleb mitme sisendi ja väljundiga mittelineaarsete diskreetaja olekuvõrrandite olekuteisendusega viimist klassikalisele vaatlejakujule. Tarvilikud ja piisavad geomeetrilised lahenduvustingimused on esitatud vektorväljade kaudu. Leitud tulemused üldistavad varasemaid mitmes aspektis: esiteks on tulemused rakendatavad ka mittepööratavatele süsteemidele; teiseks kehtivad need peaaegu kõikjal, mitte ainult süsteemi tasakaalupunkti ümbruses. Üldistused on võimalikud tänu teistsuguse matemaatilise aparatuuri kasutamisele. Piisavuse tõestus annab ühtlasi meetodi olekuteisenduse leidmiseks. Tulemusi illustreeritakse kahe näite abil [ABSTRACT FROM AUTHOR]
Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 192025200
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PubType: Academic Journal
PubTypeId: academicJournal
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  Label: Title
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  Data: Classical observer form for discrete-time nonlinear system: MIMO case.
– Name: TitleAlt
  Label: Alternate Title
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  Data: Mitme sisendi ja väljundiga diskreetse mittelineaarse juhtimissüsteemi klassikaline vaatlejakuju.
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  Data: <searchLink fieldCode="AR" term="%22Kaldmäe%2C+Arvo%22">Kaldmäe, Arvo</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Kaparin%2C+Vadim%22">Kaparin, Vadim</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Kotta%2C+Ülle%22">Kotta, Ülle</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Mullari%2C+Tanel%22">Mullari, Tanel</searchLink><relatesTo>2</relatesTo><i> tanel.mullari@taltech.ee</i><br /><searchLink fieldCode="AR" term="%22Tõnso%2C+Maris%22">Tõnso, Maris</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Proceedings+of+the+Estonian+Academy+of+Sciences%22">Proceedings of the Estonian Academy of Sciences</searchLink>. 2026, Vol. 75 Issue 1, p2-14. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Discrete-time+systems%22">Discrete-time systems</searchLink><br /><searchLink fieldCode="DE" term="%22Coordinate+transformations%22">Coordinate transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Vector+fields%22">Vector fields</searchLink><br /><searchLink fieldCode="DE" term="%22Observability+%28Control+theory%29%22">Observability (Control theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+approach%22">Geometric approach</searchLink>
– Name: Abstract
  Label: Abstract (English)
  Group: Ab
  Data: The paper addresses the problem of transforming multi-input multi-output discrete-time nonlinear state equations into the classical observer form using state transformation. Necessary and sufficient geometric solvability conditions are given in terms of vector fields. The results obtained generalize the previous ones in several aspects. First, the results are also applicable to non-reversible systems. Second, they hold almost everywhere, not only around the equilibrium point of the system. The generalizations are possible due to the use of different mathematical tools. The proof of sufficiency also provides a method for finding the state transformation. The results are illustrated by two examples. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label: Abstract (Estonian)
  Group: Ab
  Data: Artikkel käsitleb mitme sisendi ja väljundiga mittelineaarsete diskreetaja olekuvõrrandite olekuteisendusega viimist klassikalisele vaatlejakujule. Tarvilikud ja piisavad geomeetrilised lahenduvustingimused on esitatud vektorväljade kaudu. Leitud tulemused üldistavad varasemaid mitmes aspektis: esiteks on tulemused rakendatavad ka mittepööratavatele süsteemidele; teiseks kehtivad need peaaegu kõikjal, mitte ainult süsteemi tasakaalupunkti ümbruses. Üldistused on võimalikud tänu teistsuguse matemaatilise aparatuuri kasutamisele. Piisavuse tõestus annab ühtlasi meetodi olekuteisenduse leidmiseks. Tulemusi illustreeritakse kahe näite abil [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.3176/proc.2026.1.01
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 2
    Subjects:
      – SubjectFull: Discrete-time systems
        Type: general
      – SubjectFull: Coordinate transformations
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Vector fields
        Type: general
      – SubjectFull: Observability (Control theory)
        Type: general
      – SubjectFull: Geometric approach
        Type: general
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      – TitleFull: Classical observer form for discrete-time nonlinear system: MIMO case.
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            NameFull: Kaldmäe, Arvo
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            NameFull: Kotta, Ülle
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            NameFull: Mullari, Tanel
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              M: 01
              Text: 2026
              Type: published
              Y: 2026
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