Filtering and Parametrization Issues in Feedback Relevant Identiication Based on Fractional Model Representations

This report discusses ltering and parametrization issues involved in the usage of fractional representations in multivariable, approximate and feedback relevant identi-cation of a possibly unstable plant operating under closed loop conditions. It will be shown that the access to any stable right coprime factorization of the plant can be gained by employing the knowledge of the controller and to perform a speciic ltering of the signals present in the closed loop system. Then a linear time invariant model with a prespeciied McMillan degree can be estimated via the identiication of a stable coprime fractional representation wherein a speciic class of parametrizations, having the same McMillan degree, has to be used. Furthermore, it will be shown that an approximate and feedback relevant estimation of a xed order linear time invariant model based on coprime factor identiication leads to an additional constraint, which can be written down explicitly and boils down to a relation between the lter used to gain access to the coprime factors of the plant and the coprime factors of the model being estimated. A possible solutions to deal with the parametrization constraint based on an update algorithm is presented here.