From Time Series to Affine Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918171164803072 |
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| author | Padoan, A. Eising, J. Markovsky, I. |
| author_facet | Padoan, A. Eising, J. Markovsky, I. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22089 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Time Series to Affine Systems Padoan, A. Eising, J. Markovsky, I. Optimization and Control Systems and Control 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. |
| title | From Time Series to Affine Systems |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2510.22089 |