{"ID":2850176,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22089","arxiv_id":"2510.22089","title":"From Time Series to Affine Systems","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.","short_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-in...","url_abs":"https://arxiv.org/abs/2510.22089","url_pdf":"https://arxiv.org/pdf/2510.22089v1","authors":"[\"A. Padoan\",\"J. Eising\",\"I. Markovsky\"]","published":"2025-10-25T00:03:01Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}