µ analysis with real parametric uncertainty

Abstract

The authors give a broad overview, from a LFT (linear fractional transformation) µ perspective, of some of the theoretical and practical issues associated with robustness in the presence of real parametric uncertainty, with a focus on computation. Recent results on the properties of µ in the mixed case are reviewed, including issues of NP completeness, continuity, computation of bounds, the equivalence of µ and its bounds, and some direct comparisons with Kharitonov-type analysis methods. In addition, some advances in the computational aspects of the problem, including a branch-and-bound algorithm, are briefly presented together with the mixed µ problem may have inherently combinatoric worst-case behavior, practical algorithms with modes computational requirements can be developed for problems of medium size (<100 parameters) that are of engineering interest.