OBSERVABILITY AND CONTROLLABILITY FOR SMOOTH NON-LINEAR SYSTEMS

The definition of a smooth nonlinear system as proposed recently by J. C. 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.