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.

Accepted:

DOI: 10.1051/m2an/2017014

Keywords: Model order reduction, error estimation

^{1}; Antoulas, Athanasios C.

^{2}; Benner, Peter

^{1}

@article{M2AN_2017__51_6_2127_0, author = {Feng, Lihong and Antoulas, Athanasios C. and Benner, Peter}, 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}, publisher = {EDP-Sciences}, volume = {51}, number = {6}, year = {2017}, doi = {10.1051/m2an/2017014}, mrnumber = {3745167}, zbl = {1382.37105}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2017014/} }

TY - JOUR AU - Feng, Lihong AU - Antoulas, Athanasios C. AU - Benner, Peter TI - Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 2127 EP - 2158 VL - 51 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2017014/ DO - 10.1051/m2an/2017014 LA - en ID - M2AN_2017__51_6_2127_0 ER -

%0 Journal Article %A Feng, Lihong %A Antoulas, Athanasios C. %A Benner, Peter %T Some a posteriori error bounds for reduced-order modelling of (non-)parametrized linear systems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 2127-2158 %V 51 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2017014/ %R 10.1051/m2an/2017014 %G en %F M2AN_2017__51_6_2127_0

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 , Volume 51 (2017) no. 6, pp. 2127-2158. doi : 10.1051/m2an/2017014. http://www.numdam.org/articles/10.1051/m2an/2017014/

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