A Dual Geometric Test for Forward-Flatness
Abstract
Forward-flatness is a generalization of static feedback linearizability and a special case of a more general flatness concept for discrete-time systems. Recently, it has been shown that this practically quite relevant property can be checked by computing a unique sequence of involutive distributions which generalizes the well-known static feedback linearization test. In this paper, a dual test for forward-flatness based on a unique sequence of integrable codistributions is derived. Since the main mathematical operations for determining this sequence are the intersection of codistributions and the calculation of Lie derivatives of 1-forms, it is computationally quite efficient. Furthermore, the formulation with codistributions also facilitates a comparison with the existing discrete-time literature regarding the closely related topic of dynamic feedback linearization, which is mostly formulated in terms of 1-forms rather than vector fields. The presented results are illustrated by two examples.
Cite
@article{arxiv.2404.02816,
title = {A Dual Geometric Test for Forward-Flatness},
author = {Bernd Kolar and Johannes Schrotshamer and Markus Schöberl},
journal= {arXiv preprint arXiv:2404.02816},
year = {2025}
}