New results on identifiability of nonlinear systems

In this paper, we recall definition of identifiability of nonlinear systems. We prove equivalence between identifiability and smooth identifiability. This new result justifies our definition of identifiability.

In a previous paper, we have established that

• If the number of observations is three or more, then, systems are generically identifiable.
• If the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic.

Also, we have completely classified infinitesimally identifiable systems in the second case, and in particular, we gave normal forms for identifiable systems. Here, we will give similar results in the first case.