Interpolation by polynomials with non-negative coefficients

Abstract

We consider the problem of determining whether a polynomial of a given order and having only nonnegative coefficients can be found to interpolate a given set of positive data. This problem arises in the design of maximally robust integrating feedback controllers for linear discrete-time plants and is also relevant to the design of nonovershooting control systems. We present an algorithm for determining whether such a polynomial exists for given interpolation data.