Some results and applications about identifiability of non-linear systems

System identification of systems based on physical laws often involves parameter estimation. So, before performing estimation problem, it is necessary to investigate its identifiability. Various theoretical approaches have been developed to analyze non linear system identifiability. For example, the tools of differential algebra have given a systematic procedure to check identifiability of small size systems [7]. A modification of this method [3], based on a differential system of observation, gives an algorithm whose complexity does not increase with the number of parameters contrary to the previous approach. In this contribution, we show how (global or local) identifiability of a non linear analytic dynamical system can be analyzed using integro-differential relations between input, output and parameters. This procedure derives from the algorithm [3] and it allows to solve more easily the case of (controlled or uncontrolled) systems with known initial conditions. Finally we use these integro-differential equations to get a first parameter estimation.