Multivariable circle criteria : an approach based on sector conditions
作者:
B. KOUVARITAKIS,
R. HUSBAND,
期刊:
International Journal of Control
(Taylor Available online 1982)
卷期:
Volume 35,
issue 2
页码: 227-254
ISSN:0020-7179
年代: 1982
DOI:10.1080/00207178208922616
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
The definition and properties of sector conditions introduced by Zames for scalar systems can be extended to the multivariable case. The present paper makes use of appropriate forms of sector conditions in conjunction with the decomposition of a linear operator into two linear operators φ and G - φ, where φ has a normal transfer function matrix ; and proposes a useful stability criterion for a class of multivariable non-linear feedback systems. The relevant stability result is developed further by a suitable interpretation of sector conditions in the frequency domain. A particular choice for φ leads to a generalization of the circle criterion in which the Nyquist plot of the frequency response of scalar systems is replaced by bands swept by circles whose centres and radii are related in a direct manner to the numerical range ofG(jω). The result has a simple graphical interpretation and lends itself to a computer implementation which can be shown to be numerically stable. The approach is also suitable for the study of stability in the face of additive perturbations in the system model. Further choices of φ lead to stability tests which are based on the direct and inverse Nyquist plots of the diagonal elements ofG(jω).
点击下载:
PDF (1056KB)
返 回