  I describe a verifiable criterion for the solvability of the 2 by 2 spectral
Nevanlinna-Pick problem with two interpolation points, and likewise for three
other special cases of the mu-synthesis problem. The problem is to construct an
analytic 2 by 2 matrix function F on the unit disc subject to a finite number
of interpolation constraints and a bound on the cost function sup {mu(F(z)):
|z| < 1}, where mu is an instance of the structured singular value of a 2 by 2
matrix.
