Continuity properties of real/complex μ

The structured singular value as an important linear algebra tool to study a class of matrix perturbation problems is addressed. It is useful for analyzing the robustness of stability and performance of uncertain, linear systems. It has been pointed out by B. Barmish et al. (28th IEEE CDC Proceedings, 1989) that, in general, the structured singular value is a discontinuous function of its argument. The author shows that if complex uncertainties are included (besides real uncertainties), then, under mild conditions, the structured singular value becomes a continuous function of the argument