The real stabilizability radius of the multi-link inverted pendulum

A multi-link inverted pendulum with an arbitrary number of v links and controlled by a single torque input is considered in this paper. It is well known that as the number of pendulum links increases, an experimental pendulum system becomes more difficult to stabilize, and this is demonstrated in this paper for a nonlinear model of a multi-link inverted pendulum system. It is conjectured that the primary reason for such an increase of difficulty is due to the poor stabilizability robustness properties of the pendulum´s linearized model as additional links are added. Using the real stability and stabilizability radius, this conjecture is confirmed