From Time Series to Affine Systems

A. Padoan; J. Eising; I. Markovsky

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arXiv · 2510.22089

From Time Series to Affine Systems

A. Padoan·J. Eising·I. Markovsky

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Abstract

The paper extends core results of behavioral systems theory from linear to affine time-invariant systems. We characterize the behavior of affine time-invariant systems via kernel, input-output, state-space, and finite-horizon data-driven representations, demonstrating a range of structural parallels with linear time-invariant systems. Building on these representations, we introduce a new persistence of excitation condition tailored to the model class of affine time-invariant systems. The condition yields a new fundamental lemma that parallels the classical result for linear systems while provably reducing data requirements. Our analysis highlights that excitation conditions must be adapted to the model class: overlooking structural differences may lead to unnecessarily conservative data requirements.

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BibTeX RIS

A. Padoan, J. Eising, I. Markovsky. 2025-10-25. From Time Series to Affine Systems. https://arxiv.org/abs/2510.22089

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