特征方程的常数项的稳定区确定法
An Approach to Determine the Stable Interval of the Constant Term of a Characteristic Equation
-
摘要: 应用多项式的增广图示知识,可以得到确定特征方程常数项an的稳定区的准则.由于an本身不参加计算,而且得到的是an稳定区,不只是一组系数的判别,所以这个判别线性系统稳定性的方法具有一定的优点.对于特征方程次数n≤10都能用公式计算.当n=5或6时判别尤为便捷若n≥11.不得不依靠解数字方程才行.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 an itself is not taken into account and because this method is to get a stable interval of an, 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 an 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.
-
[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). -
点击查看大图
计量
- 文章访问数: 1871
- HTML全文浏览量: 54
- PDF下载量: 644
- 被引次数: 0
下载:
