  We give a solvability criterion for a special case of the $\mu$-synthesis
problem. That is, we prove the necessity and sufficiency of a condition for the
existence of an analytic $2 \times 2$ 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.
