Feedback Linearizable Discretizations of Second Order Mechanical Systems using Retraction Maps

Mechanical systems, in nature, are often described by a set of continuous-time, nonlinear, second-order differential equations (SODEs). This has motivated designs of various control laws implemented on digital controllers, consequently requiring numerical discretization schemes. Feedback linearizability of such sampled systems depends on the discretization scheme or map choice. In this article, we utilize retraction maps and their lifts to construct feedback linearizable discretizations for SODEs, which can be applied to various mechanical systems.