# On a Continuous-Time Version of Willems' Lemma

arXiv: https://arxiv.org/abs/2203.03702 · HTML: https://mlsanity.com/paper/2203.03702/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [An Efficient Off-Policy Reinforcement Learning Algorithm for the Continuous-Time LQR Problem](https://mlsanity.com/paper/2303.17819/) (2023)

## Abstract (arXiv)

In this paper, a method to represent every input-output trajectory of a continuous-time linear system in terms of previously collected data is presented. This corresponds to a continuous-time version of the well-known Willems' lemma. The result is obtained by sampling the continuous signals at regular intervals, and constructing Hankel-like structures that closely resemble their discrete-time counterparts. Then, it is shown how to use measured persistently excited data to design a time-varying vector of parameters that allows the generation of arbitrary piecewise differentiable trajectories. A class of input signals that satisfies the conditions for persistence of excitation is also provided.