System identification for a particular approach reduces to system reduction, determining for a system with a high state-space dimension a system of low state-space dimension. For Gaussian systems the problem of system reduction is considered with the divergence rate criterion. The divergence or Kullback-Leibler pseudo-distance corresponds to the expected value of the negative natural logarithm of the likelihood function. System reduction for Gaussian systems is thus a certainty equivalent way of maximum likelihood identification. An algebraic method is proposed for system reduction. The results are a theorem that this problem reduces to an infimization problem for a rational function for which programs are available and a procedure for computing the best approximant w.r.t. the divergence rate criterion. As illustration two examples of system reduction are presented.

System identification (msc 93E12), System identification (msc 93B30)
Life Sciences (theme 5), Energy (theme 4)
Modelling, Analysis and Simulation [MAS]
Scientific Computing

Jibetean, D, & van Schuppen, J.H. (2003). An algebraic method for system reduction of stationary Gaussian systems. Modelling, Analysis and Simulation [MAS]. CWI.