On the observability of discrete-time dynamic systems — A geometric approach

A coordinate-free description for dynamic systems described by explicit (nonlinear) difference equations in one independent variable via a differential geometric framework is presented. Based on this covariant approach suitable geometric objects for discrete-time dynamics are introduced. Especially, the observability along a trajectory is discussed and transformations to normal forms are derived. In addition, the obtained (local) observability criteria can be checked by computer algebra algorithms. Some examples illustrate the proposed approach.