### 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

**for descriptor systems:**

*E***Edx(t)/dt = Ax(t) + Bu(t), y(t) = Cx(t) + Du(t)**

If ** D, C ** or

**are not given, it means that**

*E***or**

*D=0*,*C=B*^{T}

*E=I*.There is also a vector of the Hankel singular values

*, a frequency vector*

**hsv***and the corresponding frequency response*

**w***. When the controllability and the observability Gramians are positive definite the data files contain two matrices*

**mag***and*

**S****, which are the Cholesky factors of the Gramians, rather than the Gramians themselves (for more details see the report).**

*R*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(*.zip) |
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

*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