  Rational observers are to be constructed for rational systems while
polynomial observers are to be constructed for polynomial systems. An observer
synthesis procedure is formulated. First an output-based rational realization
is synthesized for the considered rational system. Then a perturbation
technique creates an observer. Finite algebraic observability of the rational
system impies the existence of a output-based rational realization. Several
examples of rational observers are provided including a polynomial system of
which the state-space dimension of the polynomial observer is strictly higher
than that of the corresponding system.
