An Approach to Determine the Stable Interval of the Constant Term of a Characteristic Equation

Wong Chia-ho

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1981 > 2(6): 659-670

Wong Chia-ho. An Approach to Determine the Stable Interval of the Constant Term of a Characteristic Equation[J]. Applied Mathematics and Mechanics, 1981, 2(6): 659-670.

Citation:

Wong Chia-ho. An Approach to Determine the Stable Interval of the Constant Term of a Characteristic Equation[J]. Applied Mathematics and Mechanics, 1981, 2(6): 659-670.

Citation:

Wong Chia-ho. An Approach to Determine the Stable Interval of the Constant Term of a Characteristic Equation[J]. Applied Mathematics and Mechanics, 1981, 2(6): 659-670.

PDF( 603 KB)

An Approach to Determine the Stable Interval of the Constant Term of a Characteristic Equation

Wong Chia-ho

Zhejiang University, Hangzhou

Received Date: 1981-03-01
Publish Date: 1981-12-15

Abstract

Abstract

In this paper, an approach is introduced to determine the stable interval of the constant term of a characteristic equation by using the theory of extended graphical representation of polynomials. Because the constant a_n itself is not taken into account and because this method is to get a stable interval of a_n, not merely to make a stability test for a set of known coefficients, this method of stability criteria has some advantages over the others. The interval of a_n can be obtained from the calculation of some algebraical expressions when n≤10 where n is the degree of the characteristic equation. It is very convenient to calculate for the cases n=5 and n=6. When n≥11, this interval can be found only by the method of numerical solutions.

FullText(HTML)

References(7)

References

[1]	Hermité,C.Le nombre des racines d'une équation algebraigue comprises entre des limites donnees,J.de Crelle(Paris),52,(1854).
[2]	Routh,E.I.A Treatise on the Stability of a Given State of Motion-Adams Prize Essay(Macmillan,1877).
[3]	Hurwitz,A.Uber die Bedinungen unter welchen eine Gleich nur Wurzeln mit negativen reellen.Teilen besitat,Mathematical Annual,46,(1895),273-284.
[4]	Nyguist,H.Regeneration Theory,Bell Syst.Tech.J.11,(1932),126-147.
[5]	Михайлов,А.В.,Метод гармонического анализа в теории регуированя.Авмомамцка ц Телемеханцка,3,(1938).
[6]	汪家訸.多项式的增广图示及其在工程控制论中的应用.应用数学和力学,第2卷第3期.(1981).
[7]	Неймарк,Ю.И.,Сгруктура D-разбиения пространства полныомов и диагоаммы вышвеградскоо и вайквнста доклады.Академиы Наук СССР,LIX,5.(1948).