TY - JOUR

T1 - Robust stability of feedback systems

T2 - A geometric approach using the gap metric

AU - Foias, Ciprian

AU - Georgiou, Tryphon T.

AU - Smith, Malcolm C.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0027702088&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027702088&partnerID=8YFLogxK

U2 - 10.1137/0331071

DO - 10.1137/0331071

M3 - Article

AN - SCOPUS:0027702088

SN - 0363-0129

VL - 31

SP - 1518

EP - 1537

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 6

ER -