Multirate systems arise in chemical engineering due to different sampling rates of signals of interest. Typically many physical variables such as flows, temperatures etc., are typically sampled at a relatively faster rate than the compositions, as an example, in a distillation column. In the context of closed-loop control, such multirate systems pose a challenging problem due to several reasons such as increased complexity in the design with tighter performance specifications. Control of multirate systems is a very challenging problem and of great practical importance in the process industry.

Lifting techniques provide a suitable framework for transforming a multirate single-input single-output (SISO)/ multi-input multi-output (MIMO) system to a single-rate MIMO system (lifted system). Lifting is essentially a transformation where a fast-rate signal is suitably rearranged to give a slow-rate signal of increased dimensionality. In a multirate system, the signals of interest at different rates are "lifted" in this fashion resulting in a single-rate system of higher input/output dimensioniality.

In this work, we present these ideas with emphasis on the theoretical issues such as intersample ripples in the continuous output, limitations on the controller gains etc., arising in multirate control based on lifting techniques. Illustrated examples for a multirate SISO system where the sampling rate of the input signal is 'n' times faster than that of the output signal will be presented.