  The notion of zero dynamics is a cornerstone of many solutions to important
control problems such as feedback linearisation and disturbance decoupling. For
a SISO affine control system with relative degree strictly less than the order
of the system, it is known that there exists a state transformation and a
feedback transformation such that the system can be transformed to a linear
system. Making use of the fibre bundle structure induced by the state
transformation we show that it is possible to define a connection on the state
manifold such that the zero dynamics can be defined as a vertical vector field.
In this formalism the zero dynamics can be understood as motions along the
fibres of a fibre bundle.
