  This paper provides a new method to solve analytic interpolation problems
with rationality and derivative constraints, occurring in many applications to
system and control. It is based on the covariance extension equation previously
proposed by Byrnes and Lindquist in a different context. A complete solution
for the scalar problem is provided, and a homotopy continuation method is
presented and applied to some problems in modeling and robust control. Some
numerical examples illustrate robustness and efficiency of the proposed
procedure.
