The Laser Interferometer Space Antenna (LISA) is a European mission for the detection of gravitational waves in space set to be launched in 2034. The mission will see the deployment of 3 spacecraft in heliocentric orbit keeping a triangular formation with side length of 2.5 million km. Laser beams are exchanged between the spacecraft by means of suitably mounted telescopes (2 per spacecraft), with the objective of synthesizing a very-large baseline interferometer. The interferometric measurements are taken between free-floating test-masses placed inside the spacecraft. Due to the nature of the scientific objectives, the mission requirements on spacecraft-spacecraft pointing precision are exceptionally strict. Moreover, the formation needs to operate in almost perfect free-fall, therefore the solar radiation pressure needs to be continuously compensated for by the on-board thrusters. Gravitational wave signals are measured in the frequency bandwidth of 20 μHz to 1 Hz, requiring the vibrations in that domain to also be eliminated both for the attitude and the displacement. The task is made possible by the gravitational reference system, a complex device that keeps the test-masses from touching the walls of the spacecraft by applying on the latter an external force through μNewton thrusters. This mode of operation is called Drag-Free and Attitude Control System (DFACS). In this thesis we attempt to study and design a DFACS for LISA using a technique called Quantitative Feedback Theory (QFT). The design process starts from the definition of the orbits, the goal orientation of the spacecraft, the sizing of the solar radiation pressure induced disturbances and the derivation of the dynamics of the 19 degrees of freedom to be controlled. Using QFT, the design process is carried out on the DFACS using separation of the dynamics. As a result, analytical equations for the calculation of the LISA commands are derived and the methods to design a control system compliant to the scientific requirements imposed on the sensitivity are shown.