Mathematics – Complex Variables
Scientific paper
2012-01-09
Mathematics
Complex Variables
19 pages. The paper is based on a talk given at the Helton 65th birthday conference, San Diego, November 2010, and summarizes
Scientific paper
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.
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