Structured singular values with nondiagonal structures. II. Computation

In part I we introduced a robust stability measure-termed generalized structured singular value. In part II we address computational issues pertaining to this notion. Our main contribution is a computational method which would render the computation of the generalized structured singular value both more efficient and potentially more accurate. As in the computation of the usual structured singular value, the key in our method is to compute an upper norm bound scaled via a similarity transformation. It is shown that this bound is as tight as those obtained elsewhere and that it can be computed considerably more efficiently. Furthermore, it is shown that this bound is actually equal to the generalized structured singular value when the uncertainty has four blocks