Conditions for the ripple-free response of multirate systems using linear time-invariant controllers

In this work, necessary and sufficient conditions are derived for multirate systems using linear time-invariant (LTI) controllers to guarantee a ripple-free response to step reference signals. These conditions correspond to constraints on the coefficients of a finite impulse response pre-filter. The analysis is facilitated by the use of the lifting technique, the modified Z -transform, and up-sampling and down-sampling operators. Several examples of feasible filters are provided to show the existence of multiple solutions to the considered problem.