Generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint

In this paper, we present a generalized entropy criterion for solving the r ational Nevanlinna-Pick problem for n + 1 interpolating conditions and the degree of interpolants bounded by n, The primal problem of maximizing this entropy gain has a very well-behaved dual problem. This dual is a convex op timization problem in a finite-dimensional space and gives rise to an algor ithm for finding all interpolants which are positive real and rational of d egree at most n, The criterion requires a selection of a monic Schur polyno mial of degree n, It follows that this class of monic polynomials completel y parameterizes all such rational interpolants, and it therefore provides a set of design parameters for specifying such interpolants. The algorithm i s implemented in state-space form and applied to several illustrative probl ems in systems and control, namely sensitivity minimization, maximal power transfer and spectral estimation.