Conditions for interpolation of stable polynomials
Résumé
This contribution addresses the problem of the interpolation of a set of positive numbers by stable real polynomials. It is shown that the interpolant preserves local positivity, monotonicity, and convexity in order to satisfy stability requirement of the interpolating polynomial. Then this issue is formulated as a nonlinear system carrying on the existence of negative real roots and positive real parameters. By considering an extension of the Farkas's Lemma and the method of Fourier-Motzkin elimination, conditions are explicitly produced for the existence of an Hurwitz polynomial that passes through all the pairs of values to interpolate.