  This paper develops sufficient conditions for the existence of global
exponential observers for two classes of nonlinear systems: (i) the class of
systems with a globally asymptotically stable compact set, and (ii) the class
of systems that evolve on an open set. In the first class, the derived
continuous-time observer also leads to the construction of a robust global
sampled-data exponential observer, under additional conditions. Two
illustrative examples of applications of the general results are presented, one
is a system with monotone nonlinearities and the other is the chemostat system.
