AbstractThis paper addresses the existence of loop gain‐phase shaping (LGPS) solutions for the design of robust digital control systems for SISO, minimum‐phase, continuous‐time processes with parametric uncertainty. We develop the frequency response properties of LGPS for discrete‐time systems using the Δ‐transform, a transform method that applies to both continuous‐time and discrete‐time systems. A theorem is presented which demonstrates that for reasonable specifications there always exists a sampling period such that the robust digital control problem has a solution. Finally, we offer a procedure for estimating the maximum feasible sampling period for LGPS solutions to robust digital co