This paper gives a method to compute a controller that places closed-loop poles in a specified region, has an order equal to the number of plant control inputs and, under some assumptions, has prescribed controller dynamics. The proposed controller samples the plant outputs at a rate faster than the rate used for updating the control inputs; it is a multirate output controller or MROC. A systematic design method is proposed to mitigate the typical high sensitivity to measurement noise of MROCs. An application to the control of lightly damped structures is described.