Remarks on Accessibility and Observability of Nonlinear Implicit Systems

This contribution presents tests, 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 acting on their solutions such that distinguished parts of the system remain unchanged. The approach being presented requires the formal integrability of 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 perfom the test for higher order systems.