Restructure sys-mor tutorial #1141
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sdrave
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Nov 27, 2020
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| .. jupyter-execute:: | ||
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| fom.gramian('c_lrcf') |
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This seems a bit cryptic here. Maybe you can add a sentence about the argument and what other values are possible.
| + C^{\operatorname{T}} C | ||
| & = 0. | ||
| \end{align*} | ||
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Maybe one sentence (and perhaps a reference), for what these Gramians are useful.
Co-authored-by: Stephan Rave <stephanrave@uni-muenster.de>
lbalicki
reviewed
Nov 28, 2020
| invertible matrix. | ||
| In particular, there exist invertible transformation matrices | ||
| :math:`T, S \in \mathbb{R}^{n \times n}` such that the realization with | ||
| :math:`\tilde{E} = S^{\operatorname{T}} E T = I`, |
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This only holds if E is invertible right? Maybe it should be mentioned that we consider an LTI system with invertible E matrix at the beginning of the paragraph.
| :math:`\hat{B} = W^{\operatorname{T}} B`, | ||
| :math:`\hat{C} = C V`. | ||
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| It is known that the reduced-order model is asymptotically stable if |
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I think it should also be mentioned that we assume the full order model to be asymptotically stable. Maybe we should do this when the LTI system is introduced in this tutorial.
docs/source/tutorial_lti_systems.rst
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| \sup_{u \neq 0} | ||
| \frac{\lVert y \rVert_{\mathcal{L}_\infty}}{\lVert u \rVert_{\mathcal{L}_2}}. | ||
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| The computation of the :math:`\mathcal{H}_2` is based on the system Gramians |
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Thanks for the comments, I made updates. |
lbalicki
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Nov 30, 2020
sdrave
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Nov 30, 2020
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This is still a work in progress. The idea is to add an LTI tutorial and for the existing BT tutorial to reuse the model from there. An IRKA tutorial could be added in a new PR