状态空间中特征值D域稳定性的结构奇异值判据  

A μ-Measurement for Statespace D-region Stability of Eigenvalues

作　　者：丛山[1] 施颂椒[1] 

机构地区：[1]上海交通大学自动控制系

出　　处：《上海交通大学学报》1993年第5期73-78,共6页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金

摘　　要：状态空间中,状态矩阵A在扰动矩阵影响下,特征值能否保持在一个预先指定的区域D中,这就是状态空间中的D域稳定性问题。本文从结构奇异值在状态空间中的对应形式出发,研究了状态空间中的D域稳定性问题.通过推广Small-μ定理,建立了状态空间中的D域稳定性的结构奇异值判据,并给出了算例.最后,分析了结构奇异值判据存在的保守性及其可能改善的途径.Given a desired region D in the complex plane containing the eigenva- lues of a state matrix A, the so-called statespace D-region stability means when A is perturbed by a perturbation matrix E, the eigenvalues of matrix A+E can still remain in region D. In this paper, E is provided to have a structure as E=G△H (G and H are the constant structure matrices, is △ perturbation.) In some other researches, when △ is a full matrix, necessary and sufficient condi- tions have been established. But if △ is further structured, such as that in the con- text of μ-method, these results are conservative. This paper develops a way to cope with the case of a more complicated △ by the generalization of the statespace small-μ theorem. After that, two examples are given to illustrate the advan- tages of the new theorem.

关 键 词：D域稳定性 结构奇异值 鲁棒控制 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]