In this thesis he addressed the controlled Lagrangian control technique in two magnetic levitation systems, these being the fundamental object of study. An analysis of the natural dynamics of three mechanical systems was made; a simple pendulum, two pendulums attached to a xed beam and an inverted pendulum on a cart, which served to understand from a physical-mathematical point of view the presentation of the Lagrangian formalism. This analysis in mechanical systems was the basis in the study of the natural dynamics of the magnetic levitation systems treated. A geometrical stability analysis was also carried out, both for the mechanical systems and for the magnetic levitation systems; this constitutes the rst novelty as a result of the work. The presentation of the controlled Lagrangian control technique was explained in detail, taking as an example the inverted pendulum system on the cart, to later be implemented in magnetic levitation systems. The results obtained were satisfactory, demonstrating with them that this control technique makes sense in magnetic levitation systems, until now simple. From the mathematical point of view, the establishment of a control law in these magnetic levitation systems guarantees their stability in the understanding that the controlled dynamics will be equal to the desired one.