Properties of Hurwitz Polynomials with Application to Stability Theory

Authors

  • Pankaj Kumar
  • Pradeep Kumar
  • Rahu Yadav

DOI:

https://doi.org/10.53555/nnms.v1i1.557

Keywords:

HURWITZ POLYNOMIALS, PROPERTIES, STABILITY THEORY

Abstract

In mathematics, a Hurwitz Polynomial , named after Adolf Hurwitz , is a polynomial whose coefficients are positive real numbers and whose roots (zeros) are located in the left half plane of the complex plane or on the j? axis, that is, the real part of every root is zero or negative. Another element of realizability is a class of polynomial known as Hurwitz polynomial which is, in fact ,the denominator polynomial of the network function satisfying certain conditions . 1. P(s) is real when s is real . 2. The roots of p(s) have real parts which are zero or negative. The arguments involve the use of complex plane geometry techniques without invoking the theory of positive paraodd functions or continued fraction expansions methods Some of the established propertiesare then applied to test for the stability of systems of differential equations.

References

. E. A Guillemin, The Mathematics of Circuit Analysis,7th edition, Oxford & IBH Publishing,1962.

. G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, McGraw,New York,1961 .

. N. Levinson and R. M. Redheffer, Complex Variable, McGraw Hill Publishing Company Limited,1980 .

. M. Marden, Geometry of Polynomials, Amer. Math. Soc,2nd edition,1996 .

. Z Zahreddine. Explicit relationships between Routh Hurwitz and Schour,Cohn types of sta.Bility, Irish Math. Soc. Bull. 29(1992),49 54

. Z. Zahreddine, An extension of the Routh array for the asymptotic stability of a system of differential equations with complex coeffcients, Applicable Analysis, 49(1993),61.72.

Published

2014-01-31

How to Cite

Kumar, P. ., Kumar, P., & Yadav, R. . (2014). Properties of Hurwitz Polynomials with Application to Stability Theory. Journal of Advance Research in Mathematics and Statistics (ISSN 2208-2409), 1(1), 01-04. https://doi.org/10.53555/nnms.v1i1.557

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