When the control system is stabilized by a stable controller, the controller is said to be a strongly stabilizing controller. While there are many design methods of stabilizing controllers, most existing methods do not consider the stability of stabilizing controllers. Because the instability of the stabilizing controllers makes closed-loop systems very sensitive to disturbances and reduces the tracking performance to reference inputs, it is required in practice to use the stable stabilizing

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... troller whenever it is possible. Youla et al. showed that not every plant can be stabilized by a stable controller and examined a design procedure for stable stabilizing controllers. However, it is better in practice to design controllers that make use of the individuality of given plants. From this perspective, Hoshikawa et al. clarified the class of strongly stabilizable plants that can be stabilized by a stable controller. However, they have not given a design method of strongly stabilizing controllers for the class of strongly stabilizable plants. This is the purpose of this paper, and to propose a design method, we clarify the parameterization of all strongly stabilizing controllers for strongly stabilizable plants.