Model-based control algorithms generally use a model of the process with fixed parameters in the synthesis of the control law and implicitly account for uncertainty in those parameters in the selection of tunable parameters in the feedback path. In this work, a notion of set-based control is introduced for SISO processes, in order to explicitly account for the uncertainty of process dynamics in the control law. The set-based controller developed from this notion is shown to be robustly stable for all process models within the set for which it is designed. This approach is applied to deadtime compensation for processes with uncertain deadtime. It is shown that by including uncertainty in the deadtime explicitly in the controller, the region of stability and the optimal guaranteed performance of the closed-loop system is enhanced as compared to a model-based controller.