Observability and Controllability for Smooth Nonlinear Systems

The definition of a smooth nonlinear system as proposed recently by Willems, is elaborated as a natural generalization of the more common definitions of a smooth nonlinear input–output system. Minimality for such systems can be defined in a very direct geometric way, and already implies a usual notion of observability, namely, local weak observability. As an application of this theory, it is shown that observable nonlinear Hamiltonian systems are necessarily controllable, and vice versa.