Structured Singular Value and 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 general case. 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 m tuples of matrices. How to effectively compute such distance in the nonconvex case (which may arise when dealing with m more than 3) is an open problem. In this thesis, in an attempt to tackle this problem, the question of graphically displaying 2- dimensional and 3-dimensional sections of the m-form numerical range is investigated.