A parameterization of simultaneous stabilizers for a pair of linear systems within a behavioral framework

In this paper, we address simultaneous stabilization problem for a pair of linear systems within a behavioral framework. First, we provide a necessary and sufficient condition for a given pair of linear systems to be simultaneously stabilizable in a behavioral framework. Second, we extract the symmetric structure of simultaneous stabilizers. Third, we give a parameterization of all of the simultaneous stabilizers. By using this parameterization, we also give a design procedure of the simultaneous stabilizers. Finally, we also give an example in order to show the validity of our results.