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Schur's Theorem on the Stability of Networks

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Schwarzweller C., Rowińska-Schwarzweller A.

Formalized Mathematics

2006

tom 14

nr 4

135-142

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.

Ograniczanie wyników

1 Formalized Mathematics

1 Rowińska-Schwarzweller A.

1 Schwarzweller C.

1 2006

Wyniki wyszukiwania

Schur's Theorem on the Stability of Networks