Testing Backward-Flatness of Nonlinear Discrete-Time Systems
Optimization and Control
2026-02-10 v1
Abstract
Despite ongoing research, testing the flatness of discrete-time systems remains a challenging problem. To date, only the property of forward-flatness - a special case of difference-flatness - can be checked in a computationally efficient manner. In this paper, we propose a systematic approach for testing backward-flatness, which is another special case of difference-flatness, and for deriving a corresponding backward-flat output. Additionally, we discuss the relationship between the Jacobian matrices associated with the flat parameterization of backward- and forward-flat systems and illustrate our results by an academic example.
Cite
@article{arxiv.2602.08385,
title = {Testing Backward-Flatness of Nonlinear Discrete-Time Systems},
author = {Johannes Schrotshamer and Bernd Kolar and Markus Schöberl},
journal= {arXiv preprint arXiv:2602.08385},
year = {2026}
}