Modeling and design of LTI controllers for multirate systems

In this paper we provide a frequency domain approach to model multirate SISO systems which facilitates design of linear time-invariant (LTI) controllers. To illustrate the approach we consider a dual-rate system with slow output measurements and fast control actions. We obtain necessary and sufficient conditions for the existence of stabilizing LTI controllers for which model matching is also achieved with a desired single-rate system. Moreover, a solution is given to the problem of parametrizing the set of such LTI controllers.