Structured Singular Value and Geometry of the m-Form Numerical Range.

Abstract

Although the question of the numerical evaluation of Doyle's structured singular value has been repeatedly addressed, it is not yet entirely resolved in the case of block structures of size larger than 3. It has been shown recently that this question can be reduced to that of iteratively computing the distance from the origin to the m-form numerical range of certain tuples of matrices. How to effectively compute such distances in the nonconvex case (which may arise when dealing with more than 3 blocks) is an open problem. In this paper, in an attempt to tackle this problem, the question of graphically displaying sections of the m-form numerical range is investigated.