 Jury stability criterion

The Jury criterion tests whether every root of a real discrete-time characteristic polynomial lies strictly inside the unit circle. For $z^2+az+b$, this is equivalent to $|b|<1$, $1+a+b>0$, and $1-a+b>0$.

The Jury stability criterion is a method used in control theory to determine the stability of discrete-time linear systems represented in the z-domain. It is particularly relevant for systems described by polynomial equations, where the roots of the characteristic polynomial (the z-transformation of the system's difference equation) are analyzed to assess stability. According to the Jury's stability criterion, the system is stable if and only if all the roots (or poles) of the characteristic polynomial lie inside the unit circle in the z-plane.