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We give a solvability criterion for a special case of the $\mu$-synthesisproblem. That is, we prove the necessity and sufficiency of a condition for theexistence of an analytic $2 \times 2$ matrix-valued function on the discsubject to a bound on the structured singular value and satisfying a finite setof interpolation conditions. To do this we prove a realization theorem foranalytic functions from the disc to the tetrablock. We also obtain asolvability criterion for the problem of analytic interpolation from the discto the tetrablock.

Analytic interpolation into the tetrablock and a $\mu$-synthesis problem