On the identifiability of bilinear systems

Estimation of the unknown parameters that characterize a bilinear system is of primary importance in many applications. By introducing a novel concept of the derivative system for a given bilinear system, it is shown that the Fisher information matrix for a data set generated by a bilinear system with additive Gaussian measurement noise can be expressed explicitly in terms of the outputs of its derivative system which is also bilinear. A connection between the identifiability of the unknown parameters and the output reachability of the derivative system is established. For a bilinear system with a piecewise constant input and uniformly sampled output data, a trackable condition is derived for local identifiability.