Structured singular value with repeated scalar blocks

The structured singular value, μ, is an important linear algebra tool to study a class of matrix perturbation problems, [Doy]. It is useful for analyzing the robustness of stability and performance of dynamical systems [DoyWS]. This paper studies uncertainty structures involving repeated scalar parameters in more detail than in [Doy]. In [DoyP], it was shown that the frequency domain μ tests of [DoyWS] can conceptually be reduced to a single constant matrix μ test, but the uncertainty structure must be augmented with a large repeated scalar block. This paper studies the properties of μ and the upper bound with these types of uncertainty blocks, and compares the frequency domain vs. state space μ based tests, assuming that the upper bound is what can be reliably computed.