Distributed spacecraft formation flying has been identified as an enabling technology by NASA and the US Air Force for several future space missions. Implementation of the distributed spacecraft formation flying concept requires tight, autonomous, cooperative, real-time control of the relative distance and attitude between the participating spacecraft. In this paper, we develop a pulse-based, periodic gain, linear control design framework, which uses only an intermittent control action and yields guaranteed closed-loop stability. The proposed framework is utilized to design linear controllers for the linearized spacecraft relative motion dynamics viz., Hill's equations. Illustrative numerical simulations are developed for formation maintenance in ideal, naturally attractive, relative orbits, to demonstrate the efficacy of the proposed approach.