Modified Nodal Analysis - Revision history

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 ==Description: Modified Nodal Analysis Model==

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	==Description: Modified Nodal Analysis Model==		==Description: Modified Nodal Analysis Model==

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	<math>B \in \mathbb{R}^{N \times M}</math>,		<math>B \in \mathbb{R}^{N \times M}</math>,
	<math>C \in \mathbb{R}^{Q \times N}</math>,		<math>C \in \mathbb{R}^{Q \times N}</math>,
	<math>A \in \mathbb{R}^{N \times N}</math>.		<math>E \in \mathbb{R}^{N \times N}</math>.

	==Citation==		==Citation==

Himpe: init mna

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{{preliminary}} 

[[Category:benchmark]]
[[Category:SLICOT]]
[[Category:Sparse]]
[[Category:MIMO]]

'''This is a stub. Please expand.'''

==Description: Modified Nodal Analysis Model==

This set of benchmark uses models resulting from [[wikipedia:Modified_nodal_analysis|modified nodal analysis]].
More details can be found in <ref name="odabasioglu98"/> and <ref name="chahlaoui02"/>.

==Origin==

This benchmark is part of the '''SLICOT Benchmark Examples for Model Reduction'''<ref name="chahlaoui05"/>.

==Data==

The system matrices <math>A</math>, <math>B</math>, <math>C</math>, <math>E</math> are available from the [http://slicot.org/20-site/126-benchmark-examples-for-model-reduction SLICOT benchmarks] page:

{| class="wikitable" style="margin: auto;"
|+ style="caption-side:bottom;"|''Table 1: Benchmark files and dimensions.''
|-
!
!Inputs
!States
!Outputs
|-
|[http://slicot.org/objects/software/shared/bench-data/MNA_1.zip MNA_1.zip]
|<math>M = 9</math>
|<math>N = 578</math>
|<math>Q = 9</math>
|-
|[http://slicot.org/objects/software/shared/bench-data/MNA_2.zip MNA_2.zip]
|<math>M = 18</math>
|<math>N = 9223</math>
|<math>Q = 18</math>
|-
|[http://slicot.org/objects/software/shared/bench-data/MNA_3.zip MNA_3.zip]
|<math>M = 22</math>
|<math>N = 4863</math>
|<math>Q = 22</math>
|-
|[http://slicot.org/objects/software/shared/bench-data/MNA_4.zip MNA_4.zip]
|<math>M = 4</math>
|<math>N = 980</math>
|<math>Q = 4</math>
|-
|[http://slicot.org/objects/software/shared/bench-data/MNA_5.zip MNA_5.zip]
|<math>M = 9</math>
|<math>N = 10913</math>
|<math>Q = 9</math>
|}

and are stored as MATLAB [https://www.mathworks.com/help/matlab/import_export/mat-file-versions.html .mat] file.

==Dimensions==

System structure:

:<math>
\begin{array}{rcl}
E\dot{x}(t) &=& Ax(t) + Bu(t) \\
y(t) &=& Cx(t)
\end{array}
</math>

System dimensions:

<math>A \in \mathbb{R}^{N \times N}</math>,
<math>B \in \mathbb{R}^{N \times M}</math>,
<math>C \in \mathbb{R}^{Q \times N}</math>,
<math>A \in \mathbb{R}^{N \times N}</math>.

==Citation==

To cite this benchmark, use the following references:

* For the benchmark itself and its data:
::Niconet e.V., '''SLICOT - Subroutine Library in Systems and Control Theory''', http://www.slicot.org

@MANUAL{slicot_mna,
title = {{SLICOT} - Subroutine Library in Systems and Control Theory},
organization = {Niconet e.V.}
address = <nowiki>{\url{http://www.slicot.org}}</nowiki>,
key = {SLICOT}
}

* For the background on the benchmark:

@ARTICLE{morOda98,
author = <nowiki>{A. Odabasioglu and M. Celik and L.T. Pileggi}</nowiki>,
title = {{PRIMA}: Passive Reduced-order Interconnect Macromodeling Algorithm},
journal = {IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems},
volume = {17},
number = {8},
pages = {645--654},
year = {1998},
doi = {10.1109/43.712097}
}

==References==

<references>

<ref name="odabasioglu98">A. Odabasioglu, M. Celik, L.T. Pileggi, [https://doi.org/10.1109/43.712097 PRIMA: Passive Reduced-order Interconnect Macromodeling Algorithm]. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 17(8): 645--654, 1998.</ref>

<ref name="chahlaoui02"> Y. Chahlaoui, P. Van Dooren, [http://eprints.maths.manchester.ac.uk/1040/1/ChahlaouiV02a.pdf A collection of Benchmark examples for model reduction of linear time invariant dynamical systems], Working Note 2002-2: 2002.</ref>

<ref name="chahlaoui05"> Y. Chahlaoui, P. Van Dooren, [https://doi.org/10.1007/3-540-27909-1_24 Benchmark Examples for Model Reduction of Linear Time-Invariant Dynamical Systems], Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 379--392, 2005.</ref>

</references>