Relative guidance algorithms for space applications were identified by several space agencies as an enabling technology for future missions development. Whenever two or more space vehicles must coordinate their motion, or a terminal rendezvous has to be performed, a robust control of the relative motion occurring between the objects is necessary. Control must guarantee operation safety, and minimize fuel consumption, since refueling operations are currently too expensive. In this context, the paper proposes an extended linearization technique to design a nonlinear H-infinity controller for the relative motion. The developed controller is designed to minimize propellant consumption and to attenuate disturbances due to typical perturbations of low Earth orbits, such as atmospheric drag and J₂ perturbation. Terminal rendezvous and formation control simulations were performed using data from realistic missions.