A Continuous-Time Generalization of the LPV Fundamental Lemma
Abstract
Controller design for physical systems directly from data is of tremendous interest in both the industry and academia. However, the research on direct data-driven control has thus far mainly focused on discrete-time linear time-invariant systems. To make the highly non-trivial step to continuous-time nonlinear systems, this paper explores an intermediate route through the framework of linear parameter-varying (LPV) systems. LPV systems can be used as a convenient surrogate for nonlinear systems to achieve systematic analysis and controller design. In this work, we generalize the LPV Fundamental Lemma for discrete-time systems towards a class of continuous-time LPV systems, achieving data-driven representations that can be used to design continuous-time LPV controllers.
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BibTeX
@misc{schmitz2026continuoustime,
title = {{A Continuous-Time Generalization of the LPV Fundamental Lemma}},
author = {Philipp Schmitz and Chris Verhoek},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07241},
eprint = {2609.07241},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07241},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A Continuous-Time Generalization of the LPV Fundamental Lemma
AU - Philipp Schmitz
AU - Chris Verhoek
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.07241
UR - https://arxiv.org/abs/2609.07241
AB - Controller design for physical systems directly from data is of tremendous interest in both the industry and academia. However, the research on direct data-driven control has thus far mainly focused on discrete-time linear time-invariant systems. To make the highly non-trivial step to continuous-time nonlinear systems, this paper explores an intermediate route through the framework of linear parameter-varying (LPV) systems. LPV systems can be used as a convenient surrogate for nonlinear systems to achieve systematic analysis and controller design. In this work, we generalize the LPV Fundamental Lemma for discrete-time systems towards a class of continuous-time LPV systems, achieving data-driven representations that can be used to design continuous-time LPV controllers.
ER -