Quality-by-design by skewed spherical structured singular value

This study develops numerical algorithms to compute an ellipsoidal set of input parameters, called a design space, that ensures that the system outputs lie within a set of design specifications in quality-by-design. The algorithm is based on a proposed skewed spherical structured singular value ν_s, for which this study derives upper bounds and proves the (scaled) main loop theorems and small-gain theorem for the Frobenius norm. Three examples are included to illustrate applications of the numerical algorithms.