STUDY ON HURWITZ STABILITY CONDITIONS OF THE CHARACTERISTIC POLYNOMIALS USING THE COEFFICIENT DIAGRAM

계수도를 이용한 특성다항식의 Hurwitz 안정조건에 관한 연구

We investigate the Hurwitz stability condition using the coefficient diagram. The coefficient diagram consists of a plot of logarithmic values of the coefficients of the characteristic polynomial versus the degree of the coresponding coefficients. The logarithmic value of the coefficient of the characteristic polynomials are plotted in the descending order. Using the Bhattacharyya, Chapellat and Keel's algorithm, the sufficient and necessary condition for Hurwitz stability are reconstructed using the coefficient diagram. With the coefficient diagram we also present some necessary or sufficient conditions for Hurwitz stability of polynomials. In addition we obtain a lower bound for the Manabe parameter $\tau$.