In this paper the stability of a closed-loop cascade control system in the trajectory tracking task is addressed. The considered plant consists of underlying second-order fully actuated perturbed dynamics and the first order system which describes dynamics of the input. The main theoretical result establishes the conditions for Lyapunov stability formulated for the perturbed cascade control structure taking advantage of the active rejection disturbance approach. In particular, limitations imposed on a feasible set of an observer bandwidth are discussed. In order to illustrate characteristics of the closed-loop control system simulation results are presented. Furthermore, the particular implementation of the cascade control algorithm is verified experimentally using a two-axis telescope mount. The obtained results confirm that the considered control strategy can be efficiently applied for a class of mechanical systems when a high position tracking precision is required.