Modified Nodal Analysis

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Description: Modified Nodal Analysis Model

This set of benchmark uses models resulting from modified nodal analysis. More details can be found in and .

Origin

This benchmark is part of the SLICOT Benchmark Examples for Model Reduction.

Data

The system matrices $A$, $B$, $C$, $E$ are available from the SLICOT benchmarks page:

Table 1: Benchmark files and dimensions.

	Inputs	States	Outputs
MNA_1.zip	$M=9$	$N=578$	$Q=9$
MNA_2.zip	$M=18$	$N=9223$	$Q=18$
MNA_3.zip	$M=22$	$N=4863$	$Q=22$
MNA_4.zip	$M=4$	$N=980$	$Q=4$
MNA_5.zip	$M=9$	$N=10913$	$Q=9$

and are stored as MATLAB .mat file.

Dimensions

System structure:

$\begin{array}{rcl}E\dot{x}(t)& =& Ax(t)+Bu(t)\\ y(t)& =& Cx(t)\end{array}$

System dimensions:

$A\in {\mathbb{ℝ}}^{N\times N}$, $B\in {\mathbb{ℝ}}^{N\times M}$, $C\in {\mathbb{ℝ}}^{Q\times N}$, $E\in {\mathbb{ℝ}}^{N\times N}$.

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 =      {\url{http://www.slicot.org}},
 key =          {SLICOT}
}

• For the background on the benchmark:

@ARTICLE{morOda98,
 author =       {A. Odabasioglu and M. Celik and L.T. Pileggi},
 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}
}