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.