Extended Observer Forms for Submersive Discrete-time Systems

Journal article (2023)

Authors

A. Simha Networked Systems - EEMCS
Vadim Kaparin Tallinn University of Technology
Tanel Mullari Tallinn University of Technology
Ulle Kotta Tallinn University of Technology
Research Group
Networked Systems (EEMCS) (TU Delft)
Standards Nonlinear dynamical systems Observers Manifolds Output feedback Discrete-time system Extended observer form Transforms Discrete-time systems Geometric methods Nonlinear observers
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Published Date

2023

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Software Technology

Research Group

Networked Systems

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.