This paper addresses the problem of designing controllers that are robust to a great uncertainty in a time constant of the plant. Plants must be represented by minimum phase rational transfer functions of an arbitrary order. The design specifications are: (1) a phase margin for the nominal plant, (2) a gain crossover frequency for the nominal plant, (3) zero steady state error to step commands, and (4) a constant phase margin for all the possible values of the time constant (T): 0 < T < infinity. We propose a theorem that defines the structure of the set of controllers that fulfil these specifications and show that it is necessary for these robust controllers to include a fractional-order PI term. Examples are developed for both stable and unstable plants, and the results are compared with a standard PI controller and a robust controller designed using the QFT methodology. (C) 2013 Elsevier Ltd. All rights reserved.