Informativity and Identifiability for Identification of Networks of Dynamical Systems

In this paper, we show how informativity and identifiability for networks of dynamical systems can be investigated using Gröbner bases. We provide a sufficient condition for informativity in terms of positive definiteness of the spectrum of external signals and full generic rank of the transfer function relating the external signals to the inputs of the predictor. Moreover, we show how generic local network identifiability can be investigated by computing the dimension of the fiber associated with the closed loop transfer function from external measurable signals to the measured outputs.