In this document are developed considerations about the design and control of a particular system located in the field of mobile robotics, called Ballbot. A Ballbot has a particular structure that allows to present a new concept of mobility, it is a dynamically stable mobile robot that must balance itself on a sphere that guarantees the omnidirectionality movement. Principally, it was analyzed a Ballbot with a ball drive-mechanism composed of three omnidirectional wheels. In the first instance, a two-dimensional modeling of the system, considered as an inverted pendulum, was studied on the two decoupled XZ, YX planes. Congruently, to achieve the system stability, a control system was developed through the use of Matlab software and its Simulink tool.