MIMO disturbance and plant uncertainty attenuation by feedback

This paper investigates the ability of feedback to reduce plant and disturbance uncertainties in the MIMO case, by solving two fundamental problems posed by Zames (1981). The approach used here is the Banach space duality theory, which leads to a dual pair of optimizations, and the introduction of two nonstandard matrix norms. In particular, the primal-dual optimization reduces naturally to approximate finite dimensional convex optimizations within the desired tolerance. While the computation of the nonstandard matrix norms are shown to be equivalent to two semi-definite programming problems. Some qualitative implications for feedback are also deduced.