On robust stability with structured time-invariant perturbations

The authors consider the problem of robust stability for uncertain systems described in terms of multiple scalar structured time-invariant perturbations, which are norm bounded. The issue addressed is the role that the type of perturbation norm plays in the robust stability conditions. To this end, the L^p-induced norm (for 1⩽p⩽∞) on the perturbations are considered, and it is shown that the structured singular value is the necessary and sufficient condition for robust stability for all these norms. It is concluded that for time-invariant perturbations, in contrast to the time-varying case, robust stability conditions seem to be independent of the type of perturbation norms