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When a plant can be stabilized by using a stable controller, the controller is said to be a strongly stabilizing controller. The importance of strong stabilizations is to solve some problems occurred by using unstable stabilizing controllers, for example, feedback control systems become high sensitive for disturbances. Parameterizations of all strongly stabilizable plants and of all stable stabilizing controllers have already proposed. However, stable stabilizing controllers designed by using their parameterization cannot specify the input-output characteristic and the feedback characteristic separately. One of the ways to specify these characteristics separately is to use a twodegree-of-freedom control system. However, the parameterization of all two-degree-of-freedom strongly stabilizing controllers has not been examined.The purpose of this paper is to propose the parameterization of all two-degree-of-freedom strongly stabilizing controllers for strongly stabilizable plants.

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