Reduced order observer for a class of non-uniformly observable systems

There exist several observers for some particular nonlinear systems, such that the norm of the estimation error decays to zero irrespective of the input. However, observability of nonlinear systems is known to be dependent on the input. This is why this paper intends to help understanding how such observers can work, by proposing sufficient conditions for a class of non-uniformly observable systems ensuring the existence of an observer stable for any input.