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2006 | 14 | 4 | 135-142
Tytuł artykułu

Schur's Theorem on the Stability of Networks

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Wydawca
Rocznik
Tom
14
Numer
4
Strony
135-142
Opis fizyczny
Daty
wydano
2006-01-01
online
2008-06-13
Twórcy
  • Institute of Computer Science, University of Gdańsk, Wita Stwosza 57, 80-952 Gdańsk, Poland
  • Chair of Display Technology, University of Stuttgart, Allmandring 3b, 70569 Stuttgart, Germany
Bibliografia
  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [3] Czesław Byliński. Binary operations. Formalized Mathematics, 1(1):175-180, 1990.
  • [4] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [5] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [6] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [7] Czesław Byliński. The modification of a function by a function and the iteration of the composition of a function. Formalized Mathematics, 1(3):521-527, 1990.
  • [8] Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
  • [9] Anna Justyna Milewska. The field of complex numbers. Formalized Mathematics, 9(2):265-269, 2001.
  • [10] Robert Milewski. The evaluation of polynomials. Formalized Mathematics, 9(2):391-395, 2001.
  • [11] Robert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461-470, 2001.
  • [12] Robert Milewski. The ring of polynomials. Formalized Mathematics, 9(2):339-346, 2001.
  • [13] Michał Muzalewski. Construction of rings and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):3-11, 1991.
  • [14] Michał Muzalewski and Lesław W. Szczerba. Construction of finite sequences over ring and left-, right-, and bi-modules over a ring. Formalized Mathematics, 2(1):97-104, 1991.
  • [15] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • [16] Piotr Rudnicki and Andrzej Trybulec. Multivariate polynomials with arbitrary number of variables. Formalized Mathematics, 9(1):95-110, 2001.
  • [17] J. Schur. Über algebraische Gleichungen, die nur Wurzeln mit negativen Realteilen besitzen. Zeitschrift für angewandte Mathematik und Mechanik, 1:307-311, 1921.
  • [18] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
  • [19] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • [20] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
  • [21] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
  • [22] Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
  • [23] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
  • [24] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [25] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [26] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [27] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-006-0017-9
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