Randomly Generated

Description

This randomly generated state-space system is a procedural SISO test system for model reduction of linear time-invariant systems from . All matrices are generated from a uniformly random distribution: the system matrix is a diagonal matrix with elements in \([-1,0]\), where as the input and output vectors are drawn from \([0,1]\). The generated systems are stable and minimal, due to structure of \(N\) disconnected subsystems.

Data

The following Matlab code assembles the above described \(A\), \(B\) and \(C\) matrix for a given state-space dimension \(N\) and optionally a seed \(S\) 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: \[ \begin{align} \dot{x}(t) &= Ax(t) + Bu(t) \\ y(t) &= Cx(t) \end{align} \]

System dimensions\[A \in \mathbb{R}^{N \times N}\], \(B \in \mathbb{R}^{N \times 1}\), \(C \in \mathbb{R}^{1 \times N}\).

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 =          {https://modelreduction.org/morwiki/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}
}

Contact

Christian Himpe