Global observability of real analytic systems

In this paper we present a sufficient condition for global observability of nonlinear systems on manifolds that generalizes Aeyels' global observability result for Morse-Smale systems. Our main theorem establishes global observability under considerably weaker assumptions than Aeyels' Morse-Smale condition. However, we have to assume additionally real analyticity of the system. With this result at hand, we re-derive and extend the work of Ghosh and Rosenthal on perspective observability of linear systems — an issue which naturally arises e.g. in computer vision. Further applications yield sufficient conditions for observability of nonlinear cascade systems and generalized double bracket flows on Grassmann manifolds.