Multi-input control systems: Explicit feedback linearization

The problem of feedback linearization of multi-input nonlinear control systems via feedback transformations is addressed. Necessary and sufficient geometric conditions were provided in the early eighties stating that a certain distribution has to be full rank and involutive. However, finding the linearizing coordinates is subject to solving a set of partial differential equations. In this paper we provide an algorithm allowing to compute explicitly the linearizing feedback transformation. The algorithm is performed using a maximum of n - 1 steps (n being the dimension of the system) and is made possible by extending the explicit solvability of the Flow-box to the Frobénius theorem. Several examples are provided.