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.

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IFAC Symposium on System Identification
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Jibetean, D, & van Schuppen, J.H. (2003). An algebraic method for system reduction of stationary Gaussian systems. In IFAC-PapersOnLine (pp. 1879–1884). doi:10.1016/S1474-6670(17)35034-6