Geodesic
Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems
Feng, Lihong1 ; Antoulas, Athanasios C.2  ; Benner, Peter1 
1 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, 39106 Magdeburg, Germany.
2 Department of Electrical and Computer Engineering, Rice University, Houston, USA.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2127-2158

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We propose a posteriori error bounds for reduced-order models of non-parametrized linear time invariant (LTI) systems and parametrized LTI systems. The error bounds estimate the errors of the transfer functions of the reduced-order models, and are independent of the model reduction methods used. It is shown that for some special non-parametrized LTI systems, particularly efficiently computable error bounds can be derived. According to the error bounds, reduced-order models of both non-parametrized and parametrized systems, computed by Krylov subspace based model reduction methods, can be obtained automatically and reliably. Simulations for several examples from engineering applications have demonstrated the robustness of the error bounds.

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DOI : 10.1051/m2an/2017014
Classification : 37M05, 65P99, 65L70, 65L80
Keywords: Model order reduction, error estimation

Feng, Lihong 1 ; Antoulas, Athanasios C. 2 ; Benner, Peter 1

1 Max Planck Institute for Dynamics of Complex Technical Systems, Sandtorstrasse 1, 39106 Magdeburg, Germany.
2 Department of Electrical and Computer Engineering, Rice University, Houston, USA. 
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     title = {Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2127--2158},
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Feng, Lihong; Antoulas, Athanasios C.; Benner, Peter. Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 6, pp. 2127-2158. doi: 10.1051/m2an/2017014

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