Pré-Publication, Document De Travail Année : 2025

Willems' Lemma Reformulations: Which Operators preserve LTI System Behavior?

Résumé

In the behavioral approach, dynamical systems are abstracted as sets of trajectories. This approach gave birth to Willems' Fundamental Lemma, which has sparked significant interest in recent years. Indeed, the Lemma has uses in data-driven control: it provides a simple data-driven representation of any LTI system based on a single input-output record. Reformulations of the Lemma have been proposed in the literature, for instance, using frequency-domain data, each time with a new and specific proof. In this note, we show that all reformulations are necessarily based on linear shift-invariant transformations, which have the fundamental property that they preserve the trajectory space of all LTI systems.
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hal-04928711 , version 1 (04-02-2025)

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  • HAL Id : hal-04928711 , version 1

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Alexandre Faye-Bedrin, Stanislav Aranovskiy, Paul Chauchat, Romain Bourdais. Willems' Lemma Reformulations: Which Operators preserve LTI System Behavior?. 2025. ⟨hal-04928711⟩
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