This thesis, carried out in collaboration with Thales Alenia Space, addressed the design, implementation, and validation of control strategies for the Drag-Free and Attitude Control System (DFACS) of the Laser Interferometer Space Antenna (LISA) mission. LISA is a space observatory based on three Spacecrafts (SC) that will use laser interferometry to detect and measure gravitational waves by precisely monitoring the relative positions of six free-falling test masses across separate spacecraft. The mission requires that, per each SC, two Test Masses (TM) remain in the so called drag-free condition, as free as possible from all non-gravitational forces. LISA presents three particularly critical phases: con- stellation acquisition, test mass (TM) release, and drag-free science operations.