The synthesis of observers is translated to the stability of the error dynamics. The simplest case is given when the observation error dynamics is linear, a condition that implies exponential stability of the error, which is translated to an appropriate calculation of eigenvalues. On the other hand, some difficulties may arise in the extension of observers to the nonlinear case. There exist very special cases, but in general, estimation error dynamics is not linear and must be stable for the observer synthesis to become feasible. In the worst-case scenario, the study of stability is extremely difficult, considering the fact that it depends on parameters from the system and the observer that are mostly unknown.