mlsanityData to 7 Oct 2026

Finite Time Identification in Unstable Linear Systems

arXiv 1710.01852 ↗First posted 5 Oct 2017eess.SY cs.SY econ.EMcited by 66

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Abstract (arXiv)

Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially regarding finite time bounds. For this setting, classical results on least-squares estimation of the dynamics parameters are not applicable and therefore new concepts and technical approaches need to be developed to address the issue. Unstable linear systems arise in key real applications in control theory, econometrics, and finance. This study establishes finite time bounds for the identification error of the least-squares estimates for a fairly large class of heavy-tailed noise distributions, and transition matrices of such systems. The results relate the time length (samples) required for estimation to a function of the problem dimension and key characteristics of the true underlying transition matrix and the noise distribution. To establish them, appropriate concentration inequalities for random matrices and for sequences of martingale differences are leveraged.

Key facts. Cited by 66 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Oct 2017.

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Citing papers per year: 2021: 13; 2022: 14; 2023: 11; 2024: 16; 2025: 7; 2026: 5.

66 papers.

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  2. 2022Learning with little mixingcited by 33
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  11. 2022Finite Sample Identification of Bilinear Dynamical Systemscited by 12
  12. 2022Regret Lower Bounds for Learning Linear Quadratic Gaussian Systemscited by 11
38 more
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  15. 2024Outlier-Robust Linear System Identification Under Heavy-tailed Noisecited by 4
  16. 2025Finite Sample Identification of Partially Observed Bilinear Dynamical Systemscited by 4
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  30. 2023Learning and Concentration for High Dimensional Linear Gaussians: an Invariant Subspace Approachcited by 1
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  38. 2025Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Datacited by 1

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