A polynomial is said to be stable if either:
The first condition defines Hurwitz (or continuoustime) stability and the second one Schur (or discretetime) stability. Stable polynomials arise in various mathematical fields, for example in control theory and differential equations. Indeed, a linear, timeinvariant system (see LTI system theory) is said to be BIBO stable if and only if bounded inputs produce bounded outputs; this is equivalent to requiring that the denominator of its transfer function (which can be proven to be rational) is stable. The denominator is required to be Hurwitz stable if the system is in continuoustime and Schur stable if it is in discretetime. Stable polynomials are sometimes called Hurwitz polynomials and Schur polynomials.
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obtained after the Möbius transformation which maps the left halfplane to the open unit disc: P is Schur stable if and only if Q is Hurwitz stable.
is Schur stable.
