The Block Superoptimal Aak Problem

Abstract This paper presents a solution to a superoptimal version of the block AAK problem Given a rational and antistable matrix function R s R s R s and a nonnegative integer k nd all superoptimal approximations Q s with no more than k poles in the right half complex plane that minimise the supremum over the imaginary axis of the singular values of the error function E s R s R s Q s with respect to lexicographic ordering Conditions are given for which the superoptimal approximation is unique In addition an a priori upper bound on the MacMillan degree of the approximation is provided The algorithm may be stopped after minimising a given number of the singular values This premature termination carries with it a predictable reduction in the MacMillan degree of the approximation The algorithm only requires standard linear algebraic computations and is therefore easily implemented