结构型摄动多项式族的不变惯性

On Invariant Inertia of a Family of Polynomials with Structured Perturbations

中文关键词  结构型摄动  多项式  根分布  不变惯性

英文关键词  structured perturbation  polynomial  root distribution  invariant inertia

中文摘要

      给了一个结构型摄动多项式族以及复平面上的稳定性区域，是否这个族在这区域的内部，边界与外部有着不变的根的数目？这是所谓的不变惯性问题，本文将予以、回答。在否定的情况下，我们要给出方法去把这族分割为一些子族使对每一子族而言它有着各自不变的惯性。

英文摘要

      Given a family of polynomials with structured perturbations, and a stability region in the complex plane, whether the family has invariant root numbers with respect to the interior, the boundary and the exterior of the region? The paper answers the so-called invariant inertia question. In a negative case, the paper gives a method which splits the family into a series of subfamilies so that every one in the series has its own invariant inertia.