THE PARALLEL PROJECTION OPERATORS OF A NONLINEAR FEEDBACK-SYSTEM

被引：38

作者：

DOYLE, JC

GEORGIOU, TT

SMITH, MC

机构：

[1] CALTECH, DEPT ELECT ENGN, PASADENA, CA 91125 USA

[2] UNIV MINNESOTA, DEPT ELECT ENGN, MINNEAPOLIS, MN 55455 USA

[3] UNIV CAMBRIDGE, DEPT ENGN, CAMBRIDGE CB2 1PZ, ENGLAND

来源：

SYSTEMS & CONTROL LETTERS | 1993年 / 20卷 / 02期

基金：

美国国家科学基金会;

关键词：

GAP METRIC; ROBUSTNESS; LOOP-SHAPING; PASSIVITY;

D O I：

10.1016/0167-6911(93)90019-3

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper defines and studies a pair of nonlinear parallel projection operators associated with a nonlinear feedback system. These operators have been seen to play an important role in the robustness and design of linear systems especially in the theory of the gap metric, the use of weighted gaps in control system design and Glover-McFarlane loop-shaping. We show that the input-output L2-stability of a feedback system amounts to a 'coordinatization' of the input and output spaces, which is also equivalent to the existence of a pair of nonlinear parallel projection operators onto the graph of the plant and the inverse graph of the controller respectively. These projections are shown to have equal norms whenever one of the feedback elements is linear. A bound on this norm is given in the case of passive systems with unity negative feedback.

引用

页码：79 / 85

页数：7

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