Description
This randomly generated state-space system is a procedural SISO test system for model reduction of linear time-invariant systems from [1]. All matrices are generated from a uniformly random distribution: the system matrix is a diagonal matrix with elements in , where as the input and output vectors are drawn from . The generated systems are stable and minimal, due to structure of disconnected subsystems.
Data
The following Matlab code assembles the above described , and matrix for a given state-space dimension and optionally a seed for the random number generator.
function [A,B,C] = rnd(N,S)
if(nargin>1 && not(isempty(S))), rand('seed',S); end;
A = spdiags(-rand(N,1),0,N,N);
B = rand(N,1);
C = rand(1,N);
end
Dimensions
System structure:
System dimensions:
, , .
Citation
To cite this benchmark, use the following references:
- For the benchmark itself and its data:
- The MORwiki Community, Randomy Generated. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Randomly_Generated
@MISC{morwiki_rnd, author = {{The MORwiki Community}}, title = {Randomly Generated}, howpublished = {{MORwiki} -- Model Order Reduction Wiki}, url = {http://modelreduction.org/index.php/Randomly_Generated}, year = {2018} }
- For the background on the benchmark:
@ARTICLE{morWilP02, author = {K. Willcox and J. Peraire}, title = {Balanced Model Reduction via the Proper Orthogonal Decomposition}, journal = {AIAA Journal}, volume = {40}, number = {11}, pages = {2323--2330}, year = {2002}, doi = {10.2514/2.1570} }
Reference
- ↑ K. Willcox and J. Peraire. "Balanced Model Reduction via the Proper Orthogonal Decomposition", AIAA Journal, 40(11): 2323--2330, 2002.