Remarks on Accessability and Observability of Nonlinear Implizit Systems

This contribution presents test, based on Lie-groups, for the accessibility and the observability of dynamic systems described by a set of implicit ordinary differential equations. It is shown that non-accessible or non-observable systems admit Lie-groups action on their solution such that distinguished parts of the system remain unchanged. The approch being presented requires the formal integrability for the system. Therefore, a short introduction to this theory is presented, as well as its application to systems of differential equations. Besides the theoretical results sketches for computer algebra based algorithms are presented that are necessary to perform the test for higher order systems.