Automatica, Vol.33, No.12, 2131-2145, 1997
Robustness analysis with full-structured uncertainties
This paper deals with mu 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 those based on non-similarity scaling, for such problems. Here we show how to map such problems into reduced size standard mu 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 mu 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.
Keywords:PRINCIPAL DIRECTION ALIGNMENT;SINGULAR-VALUE;NONDIAGONAL STRUCTURES;FEEDBACK-SYSTEMS;MU-PROBLEM;STABILITY;PERTURBATIONS