stable polynomial

Stable polynomials arise in control theory and in mathematical theory of differential and difference equations.

Necessary condition: a Hurwitz stable polynomial (with real coefficients) has coefficients of the same sign (either all positive or all negative).

It is conjectured that a similar condition involving stable polynomials may determine whether or not the spectrum is empty for algebraic numbers a of all degrees.

We take for D the open unit disk, which means we are looking for the distance between a polynomial and the set of Schur stable polynomials.