  We investigate global dynamic feedback stabilization from a topological
viewpoint. In particular, we consider the general case of dynamic feedback
systems, whereby the total space (which includes the state space of the system
and of the controller) is a fibre bundle, and derive conditions on the topology
of the bundle that are necessary for various notions of global stabilization to
hold. This point of view highlight the importance of distinguishing trivial
bundles and twisted bundles in the study of global dynamic feedback
stabilization, as we show that dynamic feedback defined on a twisted bundle can
stabilize systems that dynamic feedback on trivial bundles cannot.
