This paper investigates the coupling of successive convex optimization guidance with robust structured H∞ control for the descent and precise landing of Reusable Launch Vehicles (RLVs). More particularly, this Guidance and Control (G&C) system is foreseen to be integrated into a nonlinear six-degree-of-freedom RLV controlled dynamics simulator which covers the aerodynamic and powered descent phase until vertical landing of a first-stage rocket equipped with a thrust vector control system and steerable planar fins. A cost function strategy analysis is performed to find out the most efficient one to be implemented in closed-loop with the robust control system and the vehicle flight mechanics involved. In addition, the controller synthesis via structured H∞ is thoroughly described. The latter are built at different points of the descent trajectory using Proportional-Integral-Derivative (PID)-like structures with feedback on the attitude angles, rates, and lateral body velocities. The architecture is verified through linear analyses as well as nonlinear cases with the aforementioned simulator, and the G&C approach is validated by comparing the performance and robustness with a baseline system in nominal conditions as well as in the presence of perturbations. The overall results show that the proposed G&C system represents a relevant candidate for realistic descent flight and precise landing phase for reusable launchers.