  Control laws for continuous-time dynamical systems are most often implemented
via digital controllers using a sample-and-hold technique. Numerical
discretization of the continuous system is an integral part of subsequent
analysis. Feedback linearizability of such sampled systems is dependent upon
the choice of discretization map or technique. In this article, for feedback
linearizable continuous-time systems, we utilize the idea of retraction maps to
construct discretizations that are feedback linearizable as well. We also
propose a method to functionally compose discretizations to obtain higher-order
integrators that are feedback linearizable.
