In this paper, leader-follower formation flying problems based on the periodic orbits of the Hill-Clohessy-Wiltshire equations are considered. For a given final relative orbit, the admissible controls are feedback controls such that the follower tracks the final orbit asymptotically. The main performance index is the L1-norm of the control input which is proportional to the fuel consumption. The L∞-norm, which gives the magnitude of the input, is an additional performance index under the thruster level limitation. Feedback controls are designed via two algebraic Riccati equations with parameters, and their L1- and L∞- norms are given as functions of the parameters. Suboptimal controls are designed by choosing appropriate parameters. Simulation results for a reconfiguration problem are given to demonstrate the effectiveness of the design method.