A geometrical linearization theory

A linearization theory that is geometrical is presented. This means that the relationship of the control vector fields to the output function is considered from a purely geometrical, global perspective. The author argues for general position, generic vector fields and output functions and linearization for typical (most) trajectories. This approach succeeds in resolving the problem of singularities and is more complex than approaches in the literatures. The unavoidable cost is that the concepts of strong relative degree and zero dynamics cannot, in general, be defined globally. A simple example is included with a common type of output function, and linearization is worked out in some detail as an illustration of some of the features of this approach