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arXiv · 2203.03702

On a Continuous-Time Version of Willems' Lemma

Victor G. Lopez·Matthias A. Müller
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Abstract

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.

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Victor G. Lopez, Matthias A. Müller. 2022-03-07. On a Continuous-Time Version of Willems' Lemma. https://doi.org/10.1109/cdc51059.2022.9992347

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