Schur stable polynomial

Summary

A Schur stable polynomial is a polynomial whose roots all lie strictly inside the unit circle of the complex plane. It is the discrete-time partner of a Hurwitz stable polynomial, whose roots lie in the open left half-plane. A linear recurrence with constant coefficients has all its solutions tending to zero exactly when its characteristic polynomial is Schur stable. So the notion is the basic test for stability of discrete-time linear systems and of numerical schemes.