Schur stability criterion

For a real monic quadratic

z^{2} + a_{1} z + a_{2}

, both roots lie in the closed unit disk when

∣ a_{2} ∣ \leq 1, 1 + a_{1} + a_{2} \geq 0, 1 - a_{1} + a_{2} \geq 0,

with the usual simplicity requirement for roots on the unit circle.

 Ancestors (5)