On Triangular Forms for x-Flat Control-Affine Systems With Two Inputs
Dynamical Systems
2026-01-08 v3 Optimization and Control
Abstract
This paper examines a broadly applicable triangular normal form for x-flat control-affine systems with two inputs. First, we show that this triangular form encompasses a wide range of established normal forms. Next, we prove that any x-flat system can be transformed into this triangular structure after a finite number of prolongations of each input. Finally, we introduce a refined algorithm for identifying candidates for x-flat outputs. Through illustrative examples, we demonstrate the usefulness of our results. In particular, we show that the refined algorithm exceeds the capabilities of existing methods for computing flat outputs based on triangular forms.
Keywords
Cite
@article{arxiv.2505.15562,
title = {On Triangular Forms for x-Flat Control-Affine Systems With Two Inputs},
author = {Georg Hartl and Conrad Gstöttner and Markus Schöberl},
journal= {arXiv preprint arXiv:2505.15562},
year = {2026}
}