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.

The data files retrievable from this page are usually archived in zip files that are compressed with Ultimate Zip. If you have any problems downloading or uncompressing the files, please click This email address is being protected from spambots. You need JavaScript enabled to view it.. The archives contain MAT-files for MATLAB 6 or later.

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
FOM model fom.mat   1006 1 1
Random example random.mat   200 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
200 1 1
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

Available Reports

  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.

This email address is being protected from spambots. You need JavaScript enabled to view it. March 4, 2002, Updated: This email address is being protected from spambots. You need JavaScript enabled to view it. August 31, 2005; June 13, 2006