Explicit feedback linearization of control systems

This paper addresses the problem of feedback linearization of nonlinear control systems via state and feedback transformations. Necessary and sufficient geometric conditions were provided in the early eighties but finding the feedback linearizing coordinates is subject to solving a system of partial differential equations and had remained open since then. We will provide in this paper a complete solution to the problem (see the companion paper where the state linearization has been addressed) by defining an algorithm that allows to compute explicitly the linearizing state coordinates and feedback for any nonlinear control system that is truly feedback linearizable. Each algorithm is performed using a maximum of n - 1 steps (n being the dimension of the system) and they are made possible by explicitly solving the Flow-box or straightening theorem. A possible implementation via software like Mathematica/Matlab/Maple using simple integrations, derivations of functions might be considered.