On the relationship between the model order reduction problem and the simultaneous stabilization problem

This note points out the fact that, under certain conditions, the model order reduction problem is very closely tied to the simultaneous stabilization problem. These conditions occur when the reduced order model is to be used to design a suboptimal controller for a high-order plant. Under these conditions the controller must not only stabilize the low-order model, but must also stabilize the high-order plant. The result concerning the existence of a controller that will simultaneously stabilize two plants is used to conclude that the approximate inclusion of any unstable real modes of the high-order plant in the low-order model will guarantee the existence of such a controller.