A new concept has been developed for designing optimal feedback controllers that will be insensitive to given, arbitrarily large variations in physical parameters. The method uses as a single figure of merit the expected value of a quadratic performance index, the minimization of which determines directly (without trial and error) the desired set of feedback gains. These values of the feedback gains (where such exist) guarantee at the outset closed-loop stability for all possible values of physical parameters in the prescribed domain of uncertainty. The new method extends the well known method for the optimal regulator design where physical parameters have single, precisely known values, to the case where they may have a range of values. In addition, it encompasses (as a special case) the Minimax design developed also for handling systems whose physical parameters may have a range of values (which the Minimax explores by trial and error while the new method accounts automatically for the entire range). An essential feature of the new procedure is that it includes exactly in its cost criterion whatever effects accompany large departures in the plant parameters from their nominal values. This is why the new method is able to guarantee stability over the whole range of parameter values, where perturbation techniques are not. The feasibility and usefulness of the new design technique are illustrated by numerical examples in which control systems are designed for second-order plants each of whose parameters may have a given range of values. Comparisons which results using standard optimal design and the Minimax technique are given. Application to high-order systems will need to be accompanied by further development of appropriate computational procedures.