mu analysis with real parametric uncertainty

Abstract

The authors give a broad overview, from a LFT (linear fractional transformation)/mu 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 mu in the mixed case are reviewed, including issues of NP completeness, continuity, computation of bounds, the equivalence of mu 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 novel branch and bound algorithm, are briefly presented together with numerical results. The results suggest that while the mixed mu problem may have inherently combinatoric worst-case behavior, practical algorithms with modest computational requirements can be developed for problems of medium size (less than 100 parameters) that are of engineering interest.