On the observability of nonlinear systems

Question

I am looking for a reference on the observability of nonlinear systems of the form $$\begin{aligned} \dot{x} &= f(x,u) \\ y &= h(x) \end{aligned}$$ As far as I remember, it should be something dual to the controllability/feedback linearization via the Lie derivatives. Unfortunately, years have passed since I touched the subject last time and, surprisingly, I cannot find anything related in my notes. I am looking, e.g., for a tutorial or lecture notes that can be given to (good) students.