This paper presents a new methodology for the optimal process and control design of dynamic systems under uncertainty. Robust feasibility and stability analyses are incorporated within the proposed methodology to ensure process dynamic operability and asymptotic stability. These analyses are formulated as convex mathematical problems; thus, the present approach is computationally attractive since it does not require the solution of an MINLP to evaluate dynamic feasibility and stability as it has been proposed by recent dynamic optimization based methodologies. A norm bounded metric based on Structured Singular Value (SSV) analysis is employed to estimate the worst case deviation in the process constraints in the presence of critical realizations in the disturbances. The robust stability Lest is based on Lyapunov theory and guarantees process asymptotic stability. Accordingly, the optimal process and control design alternative obtained by the method proposed here is dynamically feasible and asymptotically stable since it accommodates the most critical realizations in the disturbances. A ternary distillation system featuring a rigorous tray-by tray process model is used to illustrate the application of the proposed method. 2013 Elsevier Ltd. All rights reserved.