Properties
- The Routh-Hurwitz theorem provides an algorithm for determining if a given polynomial is Hurwitz stable.
- To test if a given polynomial P (of degree d) is Schur stable, it suffices to apply this theorem to the transformed polynomial
obtained after the Möbius transformation which maps the left half-plane to the open unit disc: P is Schur stable if and only if Q is Hurwitz stable.
- Necessary condition: a Hurwitz stable polynomial (with real coefficients) has coefficients of the same sign (either all positive or all negative).
- Sufficient condition: a polynomial with (real) coefficients such that:
is Schur stable.
- Product rule: Two polynomials f and g are stable (of the same type) if and only if the product fg is stable.
Read more about this topic: Stable Polynomial
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