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Mathematics > Numerical Analysis

arXiv:2404.10511 (math)
[Submitted on 16 Apr 2024]

Title:Balancing-based model reduction for switched descriptor systems

Authors:Mattia Manucci, Benjamin Unger
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Abstract:We present a novel certified model order reduction (MOR) algorithm for switched descriptor systems applicable to large-scale systems. Our algorithm combines the idea of [Hossain \& Trenn, Technical report, 2023] to reformulate the switched descriptor system as a switched ordinary differential equation with jumps and an extension of the balanced truncation for switched ODE from [Pontes Duff et al., IEEE Trans.~Automat.~Control, 2020]. Besides being the first MOR method for switched descriptor systems applicable to the large-scale setting, we give a detailed numerical analysis by incorporating the error in the computation of the system Gramians in the a-priori error bound for the output of the reduced system. In more detail, we demonstrate, theoretically and numerically, that the standard error bound is not applicable, and a certificate must account for the numerical approximation errors.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65F45, 65F55, 65P99, 93A30, 93A15, 93B99
Cite as: arXiv:2404.10511 [math.NA]
  (or arXiv:2404.10511v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2404.10511

Submission history

From: Mattia Manucci [view email]
[v1] Tue, 16 Apr 2024 12:32:55 UTC (91 KB)
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