The controllability of a double inverted pendulum by symbolic algebra analysis

The use of computational symbolic algebra, when applied to the mechanical system described by the inverted pendulum of two links, yields formal controllability results which retain full symbolic generality in the system´s physical mass and length variables. It is shown that only a single, time-varying horizontal force, applied to the moving base of the system, suffices to theoretically realize control. Supporting analysis is presented for the trivial single link ease, in which a similar result is seen to hold, and some initial aspects of controllability are also discussed, based on these results, with reference to the more complex multi-link inverted pendulum