This note describes a method for generating an infinite-dimensional family of nonlinear control laws for underactuated systems. For a ball and beam system, the entire family is found explicitly.
@article{arxiv.math/0003177,
title = {Matching control laws for a ball and beam system},
author = {F. Andreev and D. Auckly and L. Kapitanski and A. Kelkar and W. White},
journal= {arXiv preprint arXiv:math/0003177},
year = {2007}
}