Towards the theoretical controllability of a friction damped multi-link inverted pendulum: the quadruple link system, N-link inferences

To date, there has been no control study dedicated explicitly to the quadruple inverted pendulum. This privation is rectified here, in an examination of the (linear) controllability of the system under viscous friction damping. Results are obtained by means of algebraic computing from an analytic dynamic description of the model, and, in the light of earlier work on systems with fewer degrees of freedom, allow illations relating to the general model of arbitrary link number; these inferences are presented in proposition format.