m-form numerical range and the computation of the structured singular value

An equivalent expressions for the structures singular value is proposed, leading to an alternative algorithm for its computation. The approach is based to the geometric properties of the m-form numerical range of certain tuples of matrices. Similar to previously considered schemes, the algorithm proposed is proved to give the correct value for block structures of size up to three. For larger sizes, insight is gained into the question of the possible gap between the structured singular value and its known upper bound