Extended Observer Forms for Submersive Discrete-time Systems

Ashutosh Simha, Vadim Kaparin, Tanel Mullari, Ulle Kotta

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—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 languageEnglish
Pages (from-to)2684-2688
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number4
Publication statusPublished - 2023

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  • 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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