Zero assignment by measurement feedback

The problem of assigning a prescribed set of zeros to the transfer function relating external inputs to controlled outputs, by a proper, stabilizing, measurement driven controller is solved for the case of scalar signals. The set of forbidden zeros is directly calculated from the zeros of the given transfer functions and this simplicity is the main contribution of this note. This is a generalization of the well-known classical result that a unity feedback linear servomechanism cannot track signals whose poles coincide with the RHP zeros of the plant.