Rational observers of rational systems

Abstract: 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.