It is often realized that the control system design utilizing modern state space theory produces unstable controllers. Such unstable controllers which should stabilize the plant theoretically, do not really stabilize the plants when they are implemented.Unstable controllers are not preferable from the view point of robustness and safety. Even if an unstable controller can stabilize the plant, it works well only when it is operating with the original plant. When some accident occurs and the feedback loop is cut, unstable motion of controller brings the worst results.In the design of control system for many aerospace vehicles and space structures, classical design methods of compensator are not applicable and only the modern techniques can be utilized, where the number of states, inputs and outputs are very large. In such cases, controllers should include high dimensional complex dynamics. Therefore the problem of strong stabilization i.e. the design of stable controller, is especially important for aerospace control problems.The purpose of this paper is to present a new convenient method to obtain a stable controller utilizing the quadratic stabilization techniques which is developed for the robust control system design.