Existence of controllers stabilizing the reduced-order model and not the plant (Q1108989)

It is shown that for each pair of different rational transfer functions there exists a controller stabilizing the first and not be second one. This implies that for each reduced-order model of a given plant, no matter how ``good'' it is, there exists a stabilizing controller not stabilizing the plant. Hence, for any odel reduction scheme, special care is required to obtain stabilizing controllers from reduced-order models.