# Schur's Theorem on the Stability of Networks

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## Schur's Theorem on the Stability of Networks

A complex polynomial is called a Hurwitz polynomial if all its roots have a real part smaller than zero. This kind of polynomial plays an all-dominant role in stability checks of electrical networks.

In this article we prove Schur's criterion [17] that allows to decide whether a polynomial p(x) is Hurwitz without explicitly computing its roots: Schur's recursive algorithm successively constructs polynomials pi(x) of lesser degree by division with x - c, ℜ {c} < 0, such that pi(x) is Hurwitz if and only if p(x) is.

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# Formalized Mathematics

## (a computer assisted approach)

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