A model-based approach for the construction of design spaces in quality-by-design

An algorithm is proposed for the characterization of the set of allowable real parametric uncertainties that achieve output specifications for nonlinear systems. The approach first expands the system output by a multivariate polynomial or rational function of perturbations of the real parameters, which is then written as a linear fractional transformation. Bounds on the uncertainty set are computed for the expansion using the skewed structured singular value. The proposed algorithm is demonstrated to be effective for the tracking problem of determining the allowable speed and angle for throwing a ball to land within a target and for a pharmaceutical crystallization in which an alternative solution method is available.