In the pharmaceutical industry, it is common to determine the maximum allowable set of uncertain parameters - called the design space - that guarantees that the product quality attributes obtained by a manufacturing process are within specified limits. In industrial practice, design spaces are constructed without considering the effects of process dynamics or feedback control, which results in poor characterization of operations. This paper presents an approach for determining the design space for a continuous-time state-space model with linear fractional uncertainties and for simultaneously synthesizing a linear feedback controller. For a set of ellipsoidal quality attributes, a parameterization of the ellipsoidal design space is proposed. Then, a robust optimal control technique is presented to ensure the ellipsoidal quality attributes are satisfied while maximizing the volume of the ellipsoidal design space. The proposed approach is illustrated in a simulation example.