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PreprintCC BY 4.0arXiv

On the Exact Linearization of Multi-Input Discrete-Time Flat Systems

  • Johannes Schrotshamer
  • Bernd Kolar
  • Markus Schöberl
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Abstract

In this contribution, we address the exact linearization of forward- and backward-flat discrete-time nonlinear systems with an arbitrary number of inputs. Building on structural properties of the flat parameterization, we show that forward-flat systems can be rendered static feedback linearizable by prolongations of suitably transformed inputs. Analogously, for backward-flat systems, we derive a constructive procedure showing that an exact linearization can be achieved by prelongations of suitably chosen functions of the system variables. In this way, we extend previously established results for two-input systems to the general m-input case. Finally, we illustrate the proposed linearization procedures by an academic example and a discrete-time model of a quadrotor.

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Cite

BibTeXRIS
BibTeX
@misc{schrotshamer2026exact,
  title = {{On the Exact Linearization of Multi-Input Discrete-Time Flat Systems}},
  author = {Johannes Schrotshamer and Bernd Kolar and Markus Schöberl},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08697},
  eprint = {2610.08697},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08697},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - On the Exact Linearization of Multi-Input Discrete-Time Flat Systems
AU  - Johannes Schrotshamer
AU  - Bernd Kolar
AU  - Markus Schöberl
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08697
UR  - https://arxiv.org/abs/2610.08697
AB  - In this contribution, we address the exact linearization of forward- and backward-flat discrete-time nonlinear systems with an arbitrary number of inputs. Building on structural properties of the flat parameterization, we show that forward-flat systems can be rendered static feedback linearizable by prolongations of suitably transformed inputs. Analogously, for backward-flat systems, we derive a constructive procedure showing that an exact linearization can be achieved by prelongations of suitably chosen functions of the system variables. In this way, we extend previously established results for two-input systems to the general m-input case. Finally, we illustrate the proposed linearization procedures by an academic example and a discrete-time model of a quadrotor.
ER  -