# Fundamental Lemma for Data-Driven Analysis of Linear Parameter-Varying Systems

arXiv: https://arxiv.org/abs/2103.16171 · HTML: https://mlsanity.com/paper/2103.16171/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2021.

## Built on by (most cited first, 2 of 2)

- [From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma](https://mlsanity.com/paper/2508.07494/) (2025)
- [k-Inductive Neural Barrier Certificates for Unknown Nonlinear Dynamics](https://mlsanity.com/paper/2605.20108/) (2026)

## Abstract (arXiv)

Based on the Fundamental Lemma by Willems et al., the entire behaviour of a Linear Time-Invariant (LTI) system can be characterised by a single data sequence of the system as long the input is persistently exciting. This is an essential result for data-driven analysis and control. In this work, we aim to generalise this LTI result to Linear Parameter-Varying (LPV) systems. Based on the behavioural framework for LPV systems, we prove that one can obtain a result similar to Willems'. Based on an LPV representation, i.e., embedding, of nonlinear systems, this allows the application of the Fundamental Lemma for systems beyond the linear class.