Disturbance Decoupling Problem for $n$-link chain pendulum on a cart system

A disturbance decoupling problem for a $n$-link chain pendulum on a cart is considered. A model of the cart developed in a coordinate-free framework and the linearized equations of this system are considered from [1]. It is shown that it is possible to design a suitable state feedback such that the angular position or velocity of the $n^{th}$-link can always be decoupled from the disturbance coming at the cart.