Let Ak, k - 1, …, m be n × n Hermitian matrices and let [image omitted] have components fk(x) = xHAkx, k=1,…,m. When n ≥ 3 and m = 3, the set W(A1 … Am)= |f(x) x2 - 1 | is convex. This property does not hold in general when m > 3. These particular cases of known results are proven here using a direct, geometric approach. A geometric characterizarion of the contact surfaces is obtained for any n and m. Necessary conditions are given for f(x) to be on the boundary of W(A, …Am) or on certain subsets of this boundary. These results are of interest in the context of the computation of the structured singular value, a recently introduced tool for the analysis and synthesis of control systems.
Tijdschrift beschrijving