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.

This report is the original submission to the 55th IEEE Conference on Decision and Control held in December 2016. The proceedings of the conference contains the six page final version. The submission has 8 pages. The submission contains two more examples but less explicit results on the performance of the observer