Properties of Hurwitz Polynomials with Application to Stability Theory

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 thetheory 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.