A new robust predictive controller design technique is developed for a general class of large deadtime processes. The proposed sub-optimal robust state analytical predictor (RSAP) is constructed from a two-step design procedure. In the first step, a linear quadratic Gaussian-based state analytical predictor (LQG-based SAP) is introduced to ensure the nominal stability and performance of the overall control system. It is then embedded into an internal model control (IMC) structure. Hence, a suitable design of the RSAP controller is obtained. The trade-off between stability and performance robustness of the original LQG-based SAP can be made well during the design steps. Some theoretical proofs regarding the internal stability properties of the system are derived by an analytical method of doubly coprime factorizations. The LQG-based SAP controller is proven to be a central stabilizing controller. A slight modification of the well-known results of the Youla’s Q-parametrization is also made for a special category of incompletely controllable systems; consequently, a set of all stabilizing controllers is obtained. Analytical derivations and proofs have indicated that the LQG-based SAP controller, obtained from the first design step, is a special design of IMC controllers and the proposed RSAP controller is a stabilizing controller. A norm-bounded criterion is provided to ascertain the dynamic resilience of the corresponding RSAP system. The promising performances regarding the disturbance rejection in the face of system nonlinearities and/or unmodelled dynamics are finally illustrated by computer simulations for a temperature control of a continuous stirred tank reactor.