(Possible) application of Sarason interpolation theorem This question is related to the following Wikipedia article on Nevanlinna–Pick interpolation. At the end it has been written as 

Pick–Nevanlinna interpolation was introduced into robust control by Allen Tannenbaum.

I do not have the access of the paper or even if I had, without any basic knowledge on control theory, I would, perhaps,  not be able to understand it. 
There is a operator theoretic avatar of the above problem, called Sarason interpolation theorem. I am interested in its finite dimensional version. Can anybody help me in understanding, how it can be used in control theory from a mathematical point of view or give some relevant references? I do not have any knowledge of control theory. This is only for my curiosity. Advanced thanks for any help/suggestion. 
 A: The simplest linear control theory deals with time signals on $[0,\infty)$, and linear differential/integral operators with constant coefficients applied to those signals. After Laplace transforming functions in $L^{2}[0,\infty)$ ($L^{2}$=finite energy,) you end up with functions which are holomorphic on the right half plane with square-integrable boundary functions along the imaginary axis (Paley-Wiener Theorem.) Equivalently, a function $f$ is the Laplace transform of an $L^{2}$ function iff it is holomorphic on the right half plane and has uniformly bounded $L^{2}$ norms on all lines in the right half plane which are parallel to the imaginary axis. Transfer functions become multipliers in this context because the Laplace transform turns the operators into multipliers.
Stability requires that the transfer functions not have poles in the right half plane, or you end up with instabilities that show when you try to evaluate the inverse Laplace transform using residues. These undamped terms $e^{rt}e^{i\omega t}$ for $r > 0$ are unacceptable; they correspond to undamped resonances or positive feedback loops. So, one typically wants to deal with multiplication by functions which are holomorphic on the right half-plane. That's part of the control of control theory.
Apparently, the desire to control is then cast in terms of finding holomorphic multipliers with positive real part on the right half plane that have prescribed values at a certain finite number of points in the right half-plane. So you're dealing with multiplier functions that map the right half plane to the right half plane and take prescribed values. By a simple Cayley transform, this can be recast in terms of finding holomorphic functions that map the unit disk into the unit disk and which take prescribed values at a certain finite number of points. That is the Nevanlinna-Pick problem.
The conditions under which such bounded holomorphic functions exist are known in terms of the Pick matrix associated with the points $\{ z_{j}\}_{j=1}^{N}$ in the unit disk and the prescribed values $\{ w_{j}\}_{j=1}^{N}$ at those points. Of course, determining when such a Pick matrix is positive semidefinite isn't so easy either, but at least the criteria is something that can be checked, and it leads to a solution of the stated control problem.
Sarason's work deals with these problems in an operator theoretic framework. The space is the classical Hardy space $H^{2}(D)$ of functions which are holomorphic in the unit disk $D$, and whose $L^{2}$ norms on concentric circles remain uniformly bounded for all radii $0 < r < 1$. This setting is equivalent to the Paley-Wiener setting of holomorphic functions on the right half-plane with uniformly bounded $L^{2}$ norms on lines parallel to the imaginary axis. He then deals with bounded multiplier functions which are holomorphic inside the disk and which take prescribed values at a prescribed number of points inside the disk.
