Algebraic Observability of Rational Systems

For nonlinear systems, the concept of observability is defined by the indistinguishability of states. In the practical implementation, the distinguishing of states is carried out via the observability map consisting of Lie derivatives. This approach is comparatively difficult for general nonlinear systems. It is also generally not clear how many elements of the observability map are required. For the class of polynomial systems, observability can be decided using methods of algebraic geometry. This paper extends these approaches to rational systems. Two different methods are proposed and illustrated with an example.