Robustness analysis for full-structured uncertainties

This paper deals with μ problems involving full-structured (rather than block-diagonal) uncertainty, i.e. uncertainty blocks where each sub-block (or element) may be an independent uncertainty. Rearranging this problem into standard (block-diagonal) form results in an explosion in the required computation, and so a number of researchers have proposed more efficient bounds, in particular the use of non-similarity scaling for such problems. Here we show how to map such problems into reduced size standard μ problems. The standard bounds applied to the reduced size problem are then shown to be at least as accurate, and require the same computational effort, as earlier techniques, with the added bonus that the standard μ upper bound is convex. Moreover this new approach is applicable in a much more general setting, allowing one to efficiently compute both robust stability and robust performance for problems involving multiple real and complex uncertainty blocks, any number of which may be full-structured