The fast-discretization is known as an approximate but efficient technique for design and analysis of sampled-data systems. In this paper, we propose a fast-discretization-based design for sampled-data critical control systems. Supposing a tracking problem or a slow-changing disturbance rejection problem, we assume that an exogenous input is a persistent and/or transient input with bound on the rate of change. It is shown that the critical constraint for such exogenous inputs can be given in the form of the inequality constraint on the unit step response. The design parameters are determined by a numerical search method subject to this constraint. However, instead of evaluating it strictly, we check the corresponding constraint which is obtained from the fast-discretized system. Although this approach is approximate, it provides an efficient numerical procedure for a computer-aided design. To show the validity of the proposed method, an example of a multi-objective critical control system design is presented.