This paper is devoted to the problem known as digital redesign, i.e. given a previously designed stabilising continuous-time controller for a continuous-time plant, synthesise a digital controller that provides the hybrid closed-loop system with output trajectories as similar as possible to the continuous-time ones. To accomplish this goal, two distinct optimisation criteria are investigated: (i) the Euclidean norm of the difference between the dynamic matrix of the discretised closed-loop continuous-time system and the dynamic matrix that represents the discretised open-loop system fed back by the designed digital controller; (ii) the norm of the transfer function from the noise input to the error between the outputs of the two systems. As main novelties with respect to the existing results on digital redesign, the proposed conditions can deal with polytopic systems, and can synthesise reduced-order dynamic output-feedback digital controllers as well.