Matching, linear systems, and the ball and beam
  A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. This basic idea is used in several papers already. In this paper, we will describe one matching condition and an approach for finding all control laws that fit the condition. After an analysis of the resulting control laws for linear systems, we will present the results from an experiment on a ball and beam system. 
Fedor Andreev, David Auckly, Lev Kapitanski, Shekhar Gosavi, Atul   Kelkar and Warren White