Modified Nodal Analysis

Modified Nodal Analysis

Background
Benchmark ID	mna_n10913m9q9 mna_n4863m22q22 mna_n578m9q9 mna_n9223m18q18 mna_n980m4q4
Category	slicot
System-Class	LTI-FOS
Parameters
nstates	10913 4863 578 9223 980
ninputs	9 22 9 18 4
noutputs	9 22 9 18 4
nparameters	0
components	A, B, C, E
Copyright
License	NA
Creator	Christian Himpe
Editor	Christian Himpe
Location
NA

Modified Gyroscope

Background
Benchmark ID	modifiedGyroscope_n17931m1q1
Category	misc
System-Class	AP-LTI-SOS
Parameters
nstates	17931
ninputs	1
noutputs	1
nparameters	3
components	B, C, E, K, M
Copyright
License	NA
Creator	Lihong Feng
Editor	Lihong Feng Christian Himpe Judith Schneider Jens Saak Kathryn Lund
Location
NA

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}
}