A model M (θ) is unidentifiable if there exist several values of the parameter vector θ which are associated with the same input-output relation. In such a situation any further use of θ is questionable. A methodology for dealing with unidentifiable state space models is proposed. Some tools are given to set up either a new experiment or a new parametrisation in order to make the model identifiable; others allow us to generate the set of all output-indistinguishable models. Compartmental models, widely used in biology, supply both the practical motivations and an example of application for the proposed methodology.
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