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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.
Packard et al. (Wed,) studied this question.