This paper examines the feasibility of implementing Linear Quadratic Gaussian (LQG) Control in structural cointegrated VAR models and sheds some light on the two major problems generated by such implementation. The first aspect to be taken into account is the effect of the presence of unit roots in the system on the policymakeru0092s ability to control it, partially or thoroughly. Different control techniques are proposed according to the extent to which the policymaker can exercise his control on the overall dynamics of the economy, i.e. depending on whether he/she can stabilize the whole system, only part of it or none of it. The second issue involves the structural form of the model. It will be shown in this paper that, in general, a systemu0092s features will change when implementing a new control rule. In particular, a controlled system will generally not retain features that should be intrinsecally invariant to policy changes (e.g., neutrality of money in the long-run).