On the gap between μ and its upper bound for systems with repeated uncertainty blocks

We examine the gap between the actual value of the structured singular value μ and the convex upper bound commonly used for uncertainty structures with repeated blocks. We show that for uncertainty structures having repeated full blocks this gap grows at least as much as (number of blocks) ¼. For the case of repeated scalar blocks we present a very simple example illustrating the fact that the gap can be infinite, even in cases having only two repeated blocks