In the future space infrastructure, the missions of refueling and capturing of the inoperative spacecraft by the orbital servicing vehicle or the space robot is considered. To achieve them, the six degrees of freedom tracking control of the chaser spacecraft is required to approach the target spacecraft. Moreover, the stability of the connected system of the chaser and target must be ensured. In this paper we derive the conditions for the feedback gains that satisfy the stability of the spacecraft system before and after the capturing separately. These conditions are described by the matrix inequalities. Then, we solve these inequalities simultaneously to yield the feedback gains. The controller thus obtained is applicable to the stabilizing problem before and after the connection. The effectiveness of control laws is verified by numerical simulations.