On linear modeling and recursive modeling: a summary

The authors´ previous investigations (1991) are briefly summarized. The problem of modeling, and recursive modeling, of linear dynamical systems using exact data is studied. The data or test functions were polynomial-exponential time series. These investigations were conducted in the behavioral framework, set forth by J.C. Willems (1991). Two problems which have been studied extensively and can be cast into the framework of exact modeling are realization and rational interpolation. The recursive realization results presented by A.C. Antoulas (1986), anticipated the ones presented by the authors in (1991). The main result of the former study remained valid in the present context: recursive update corresponds to attaching an appropriately defined component to a cascade interconnection of systems. The present results can be regarded as a sweeping generalization of the results of A.C. Antoulas (1986)