Subclasses of Herglotz-Nevanlinna matrix-valued functions and linear systems

We study Herglotz-Nevanlinna matrix-valued functions that are linear-fractional transformations of the transfer matrix-valued functions of some type of linear, stationary dynamical systems. We introduce the family Fκ of Herglotz-Nevanlinna matrix-valued functions N such that the associated kernel N(Z)-N(w)/z-w N(w)-N(z)/κ is positive in the open upper half-plane. We characterize these functions in terms of Schur functions. This allows us to solve the bitangential interpolation problem in the class Fκ Finally, we consider an associated automorphism of rational unitary functions using state space methods.