Computational complexity of real structured singular value in lp setting

This paper studies a generalized real structured singular value (μ) problem where uncertain parameters are bounded by an l_p norm. Two results are presented. The first one shows that this generalized μ problem is NP-hard for any given rational number p∈[1, ∞]. The NP-hardness holds as long as le, the size of the largest repeated block, exceeds one. This result generalizes the known NP-hardness result for the conventional μ problem (with p=∞). The second result, which strengthens the first one, considers the approximability problem of the generalized μ. We show that the problem of obtaining an estimate for the generalized μ with some guaranteed bounds on the relative error remains to be NP-hard, regardless how large this bound is.