Global Identifiability of Linear Models

Abstract

This chapter describes a method [W1, W6 — W9] for testing linear time-invariant models for s.g. identifiability, as a result of a study on compartmentaI models. When dealing with such models, one can frequently consider the experiment to be composed of a sequence of elementary experiments, each of which entails observing in compartment i the result of a unit impulse injection of tracer in compartment j, which may or may not be different from compartment i. The resulting output then corresponds to one entry of the transition matrix Ф associated with the considered model. This has led us to study the properties of these matrices in order to see to what extent the knowledge of some entries of a given transition matrix enables reconstruction of the others, thus making the model c.g.i..