In quantitative feedback theory (QFT) the plant uncertainty is defined by a setP= {P} ofpossible plants. The problem is to guarantee that the system response is in a specified acceptable setA, for allPinP. QFT has been developed for large classes of plants imbedded in continuous feedback structures. This paper extends QFT to sampled-data structures. A central problem is to find the minimum sampling frequency (ωs)minneeded. The greater the plant uncertainty and the narrower the performance tolerances, the larger must ( ωs)minbe. The detailed design procedure parallels very closely that for continuous systems, by using the complex variable w, which maps the unit circle in thez-domain to the imaginary axis in thew-domain.