On uniform observation of nonuniformly observable systems

In [4, 7, 9, 12], classes of nonlinear systems are considered for which observers can be designed. Although observability of nonlinear systems is known to be dependent on the input, the proposed observers have the property that the estimation error decays to zero irrespective of the input. In the first part of this paper, it is shown that this phenomenon follows from a common property of these systems: for all of them, the ''unobservable states'' with respect to some input, are in some sense ''stable'' (in the linear case, these systems are called detectable), and for this reason, a reduced order observer can be designed. In the second part is given a more general class of nonlinear systems for which such an observer can be designed.