Analytic Interpolation into the Tetrablock and a μ-synthesis Problem

Abstract

We give a solvability criterion for a special case of the μ-synthesis problem. That is, we prove the necessity and sufficiency of a condition for the existence of an analytic 2 × 2 matrix-valued function on the disc subject to a bound on the structured singular value and satisfying a finite set of interpolation conditions. To do this we prove a realization theorem for analytic functions from the disc to the tetrablock. We also obtain a solvability criterion for the problem of analytic interpolation from the disc to the tetrablock.