Computational complexity and related topics of robustness margin calculation using μ theory: A review of theoretical developments

This paper provides a comprehensive overview of research related to computational complexity of structured singular value (a.k.a. ) problems. A survey of computational complexity results in problems is followed by a concise introduction to computational complexity theory that is useful to characterize the eywords: athematical systems theory obust control omputational complexity inherent difficulty of solving an optimization. Results on the study for NP-hardness of -approximation of problems are discussed and conservatism of convex upper-bounds including ones obtained from absolute stability theory is studied. NP-hardness of computation and conservatism of convex upper-bounds open new research trends. In particular, we give an overview of polynomial-time model reduction methods and probabilistic randomized algorithms that have been active research topics since the mid-1990s.