  In this thesis, we provide new insights into the theory of cascade feedback
linearization of control systems. In particular, we present a new explicit
class of cascade feedback linearizable control systems, as well as a new
obstruction to the existence of a cascade feedback linearization for a given
invariant control system. These theorems are presented in Chapter 4, where
truncated versions of operators from the calculus of variations are introduced
and explored to prove these new results. This connection reveals new geometry
behind cascade feedback linearization and establishes a foundation for future
exciting work on the subject with important consequences for dynamic feedback
linearization.
