The Robust Hurwitz Design Problem

近年来，对于数学描述中含有不确定参数的系统的鲁棒控制问题引起了人们的广泛关注。这种类型的不确定性出现在各种应用领域，如飞行控制、过程控制、车辆控制和网络设计。将探讨与这一主题有关的几个基本问题。这里的争论是，这种类型的许多问题(如稳定、跟踪、对寄生虫的补偿等)。可以归结为关于多项式的更基本的问题。为此，本研究首先在鲁棒控制问题和一类特殊的多项式问题之间建立了牢固的联系。由此得到的多项式具有一种特殊的结构，这将在拟议的研究中得到大量的阐述。统一的多项式框架很容易适应顺序和不确定性的变化，这些变化范围在一个连续统而不是一个有限的集合上。其目的是制定具体的补偿器设计程序。数值方法的发展在很大程度上源于哈里托诺夫最近在区间多项式理论上的突破。

Recently, considerable attention has been given to problems related to the robust control of systems whose mathematical description includes uncertain parameters. This type of uncertainty arises in a diversity of application areas such as flight control, process control, vehicle control, and network design. Several fundamental issues related to this topic will be explored. The contention here is that many problems of this type (such as stabilization, tracking, compensation against parasitics, etc.) can be reduced to more basic questions about polynomials. To this end, this research first establishes a solid connection between robust control problems and a special class of polynomial problems. The resulting polynomials turn out to have a special structure which will be heavily expoited in the proposed research. The unifying polymial framework readily accommodates changes in order and uncertainties which range over a continuum rather than a finite set. The intention is to develop specific compensator design procedures. Much of the impetus for the development of numerical methods is derived from a recent breakthrough in the theory of interval polynomials by Kharitonov.