The paper describes the development of a weighted minimum-variance control law with application to single-input single-output systems in which the control is applied at a slower rate than the available measurements of the plant output signal. The theory is extended to incorporate dynamic compensation in the controller and to encompass generalized system models. A time-domain modelling approach is employed, whereby the system dynamics and sampling operations are defined as a series of cyclically time-varying difference equations. The technique, in which the cost functions penalize both the control and a set of output signals, generates straightforward expressions for the closed-loop characteristic polynomial and is accordant with pole-placement synthesis methods. The control law suffers from similar difficulties with respect to non-minimum phase systems as its single-rate counterpart.