Necessary conditions for robust stability of a class of nonlinear systems

被引：6

作者：

Goncalves, JM ^{[1
]}

Dahleh, MA ^{[1
]}

机构：

[1] MIT, Dept EECS, Cambridge, MA 02139 USA

来源：

AUTOMATICA | 1998年 / 34卷 / 06期

基金：

美国国家科学基金会;

关键词：

robust stability; nonlinear systems; perturbations; small gain theorem; monotone stability;

D O I：

10.1016/S0005-1098(97)00231-8

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Input-output stability results for feedback systems are developed. Robust stability conditions are presented for nonlinear systems with nonlinear uncertainty defined by some function (with argument equal to the norm of the input) that bounds its output norm. A sufficient small gain theorem for a class of these systems is known. Here, necessary conditions are presented for the vector space (l(infinity), parallel to.parallel to(infinity)). These results capture the conservatism of the small gain theorem as it is applied to systems that do not have linear gain. The theory is also developed for the case of l(2) Signal norms, indicating some difficulties which make this case less natural than l(infinity). (C) 1998 Elsevier Science Ltd. All rights reserved.

引用

页码：705 / 714

页数：10

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