CONNECTIONS BETWEEN L_2-MODEL REDUCTION AND BALANCED TRUNCATION

摘要

In this paper we investigate the connection between model reduction by balanced truncation and by L_2 reduction. We show that locally, i.e., close to the set of lower order systems, balanced truncation and (unweighted) L_2 model reduction produce models that are almost identical. This implies that high order estimated models can be reduced by either L_2 reduction or balanced truncation, both methods giving a low order model with the same asymptotic varaiance, if the true data generating model is in the class of low order models.