周口师范学院学报
週口師範學院學報
주구사범학원학보
Journal of Zhoukou Normal University
2007年
2期
40~42
,共null页
复系数多项式 凸组合 鲁棒稳定性
複繫數多項式 凸組閤 魯棒穩定性
복계수다항식 철조합 로봉은정성
Convex combinations of complex polynomials; segment of complex polynomials; Robust Hurwitz stability
两个给定的同次复系数多项式是Hurwitz稳定的，它们的凸组合是否也是Hurwitz稳定的？本文就此给出了一个检验方法．该方法以结式理论为依据，并应用了Sturm定理，不需求解多项式的根，仅经过有限步的运算就可完成对凸组合的稳定性判别，应用方便．
兩箇給定的同次複繫數多項式是Hurwitz穩定的，它們的凸組閤是否也是Hurwitz穩定的？本文就此給齣瞭一箇檢驗方法．該方法以結式理論為依據，併應用瞭Sturm定理，不需求解多項式的根，僅經過有限步的運算就可完成對凸組閤的穩定性判彆，應用方便．
량개급정적동차복계수다항식시Hurwitz은정적，타문적철조합시부야시Hurwitz은정적？본문취차급출료일개검험방법．해방법이결식이론위의거，병응용료Sturm정리，불수구해다항식적근，부경과유한보적운산취가완성대철조합적은정성판별，응용방편．
Given that two complex polynomials of the same degree are Hurwitz, a test based on the application of the resultant theory and Sturm＇s theorem is advanced to determine whether the set formed from the convex combination of the two polynomials is also Hurwitz. The presented method is easy to implement. Moreover, it accomplishes the test in a finite number of arithmetic operations without having to invoke any numerical root-finding procedure.
