Approximate identification with linear regression models

Linear regression models are analysed in the least-squares identification of linear multivariable finite-dimensional models. Using the concept of system behaviour, the identification problem is formulated in a deterministic signal-oriented framework, showing clearly the distinction between problems of identification (choice of model sets) and of parametrization. In order to obtain nontrivial identified models, the identification criterion should be able to distinguish between the different models in the set. This requirement of discriminability puts restrictions on the model sets to be considered. Sets of sufficient conditions are formulated, in terms of the polynomial representations of the models, while it is noted that the identified models finally obtained are essentially dependent on the restrictions chosen. The problem discussed is shown to be closely related to the problem of constructing identifiable parameterizations for model sets described in (forward or backward) polynomial forms