A modification of the classical Nevanlinna-Pick interpolation algorithm with applications to robust stabilization

Abstract

A modification is presented of the classical Nevanlinna-Pick interpolation algorithm for bounded-analytic functions which permits interpolation with bounded-real functions. This is an essential modification when the Nevanlinna-Pick theory is applied to problems such as robust stabilization [2], since otherwise compensator transfer functions will in general have complex coefficients when complex interpolation points are present. The theory underlying the modification presented is based on the theory developed by Youla and Saito [4] on interpolation with positive-real functions. The results are applied to a numerical problem in robust stabilization.