Benchmark Examples for Model Reduction of Linear Time Invariant Dynamical Systems
In order to test the numerical methods for model reduction we present here a benchmark collection, which contains some useful "real world" examples reflecting current problems in applications.
Every data file contains the default matrices A, B, C, D and E for descriptor systems:
Edx(t)/dt = Ax(t) + Bu(t),
y(t) = Cx(t) + Du(t)
If D, C or E are not given, it means that D=0, C=BT or E=I.
There is also a vector of the Hankel singular values hsv, a frequency vector w and the corresponding frequency response mag. When the controllability and the observability Gramians are positive definite the data files contain two matrices S and R, which are the Cholesky factors of the Gramians, rather than the Gramians themselves (for more details see the report).
We give here three kinds of models: dense models, sparse models and second order models (see the report for a detailed description of each one).
The following table give the data files with a short description, if you want to download the entire data files click here.
|data||name of file
|description||order N||inputs m||outputs p|
|Eady example||eady.mat||model of an atmospheric storm track||598||1||1|
|Transmission line model||tline.mat||example of a transmission line model||256||2||2|
|CD player||CDplayer.mat||classical CD player model||120||2||2|
|PEEC model||peec.mat||partial element equivalent circuit model||480||1||1|
|PDE example||pde.mat||partial differential equation||84||1||1|
|Heat equation (continuous case)||heat-cont.mat||heat equation in a thin rod||200||1||1|
|Heat equation (discrete case)||heat-disc.mat||discretization of the previous equation||200||1||1|
|Orr-Somerfeld example||Orr-Som.mat||Orr-Sommerfeld operator
for Couette flow
|MNA example - 1||MNA_1.mat||Modified Nodal Analysis model||578||9||9|
|MNA example - 2||MNA_2.mat||"||9223||18||18|
|MNA example - 3||MNA_3.mat||"||4863||22||22|
|MNA example - 4||MNA_4.mat||"||980||4||4|
|MNA example - 5||MNA_5.mat||"||10913||9||9|
|International space station||iss.mat||component 1r of the International Space Station||270||3||3|
|Building model||build.mat||motion problem in a building||48||1||1|
|Clamped beam model||beam.mat||Clamped beam model||348||1||1|
- Younès Chahlaoui and Paul Van Dooren: A collection of benchmark examples for model reduction of linear time invariant dynamical systems; SLICOT Working Note 2002-2: February 2002.