Mark Levi has written about these things on SIAM and has a nice video up on, http://www.personal.psu.edu/mxl48/Inverted_Pendulum.html http://www.personal.psu.e

Mark Levi has written about these things on SIAM and has a nice video up on, http://www.personal.psu.edu/mxl48/Inverted_Pendulum.html http://www.personal.psu.edu/mxl48/Inverted_Pendulum.html I think they've also shown that this is robustly stable for a particular family.