ROBUST STABILITY OF FEEDBACK-SYSTEMS - A GEOMETRIC APPROACH USING THE GAP METRIC

被引:55
作者
FOIAS, C
GEORGIOU, TT
SMITH, MC
机构
[1] UNIV MINNESOTA,DEPT ELECT ENGN,MINNEAPOLIS,MN 55455
[2] UNIV CAMBRIDGE,DEPT ENGN,CAMBRIDGE CB2 1PZ,ENGLAND
关键词
ROBUST STABILIZATION; GAP METRIC; GRAPH TOPOLOGY; GRAPHABILITY; STABILIZABILITY;
D O I
10.1137/0331071
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A geometric framework for robust stabilization of infinite-dimensional time-varying linear systems is presented. The uncertainty of a system is described by perturbations of its graph and is measured in the gap metric. Necessary and sufficient conditions for robust stability are generalized from the time-invariant case. An example is given to highlight an important difference between the obstructions, which limit the size of a stabilizable gap ball, in the time-varying and time-invariant cases. Several results on the gap metric and the gap topology are established that are central in a geometric treatment of the robust stabilizability problem in the gap. In particular, the concept of a ''graphable'' subspace is introduced in the paper. Subspaces that fail to be graphable are characterized by an index condition on a certain semi-Fredholm operator.
引用
收藏
页码:1518 / 1537
页数:20
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