STRUCTURED SINGULAR-VALUES WITH NONDIAGONAL STRUCTURES .1. CHARACTERIZATIONS

The purpose of this two-part series is to provide a robustness analysi s framework for a class of problems with highly structured modeling un certainties. This framework is more general than that of the usual blo ck, diagonally structured uncertainties, and it corresponds to a struc ture consisting of block-by-block matrix perturbations. We study the s tructured singular value with respect to this structure, and we establ ish a number of novel results for this notion. Specifically, Part I co ntains a study on the properties of the structured singular value, We give an alternative characterization of this notion as the solution of a smooth optimization problem. Furthermore, we show that under a cert ain circumstance the structured singular value reduces to a vector-ind uced matrix norm. Part II then addresses computational issues associat ed with the structured singular value. Our results are useful in that they not only extend the previous work but also provide both new insig hts and an improved computational method for this class of problems.