Article Dans Une Revue IEEE Control Systems Letters 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 the celebrated Willems' Fundamental Lemma, for which various reformulations have been proposed in the literature, for instance, using frequency-domain data. 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. Our results unify the existing reformulations and provide guidelines for designing novel ones.

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Dates et versions

hal-04928711 , version 1 (04-02-2025)
hal-04928711 , version 2 (16-05-2025)

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Alexandre Faye-Bédrin, Paul Chauchat, Stanislav Aranovskiy, Romain Bourdais. Willems' Lemma Reformulations: Which Operators Preserve LTI System Behavior?. IEEE Control Systems Letters, 2025, pp.1-1. ⟨10.1109/LCSYS.2025.3570558⟩. ⟨hal-04928711v2⟩
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