关键词: 凸多面体多项式族, 区间多项式族, 菱形多项式族, 鲁棒振动性, 顶点检验

Abstract: The robust oscillation for some polynomials' families is discussed. A vertex verification result for the robust oscillation of polytopic polynomial family, under some conditions, is obtained. Moreover, the number of vertex polynomial to be checked can be reduced for interval polynomial family and diamond polynomial family. A counter-example is given to show that these vertex verification results can't be directly generalized for root distribution invariance of polynomial families.

Key words: polytopic polynomial family, interval polynomial family, diamond polynomial family, robust oscillation, vertex verification