ROBUST STABILITY OF FEEDBACK-SYSTEMS - A GEOMETRIC APPROACH USING THEGAP METRIC

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 highl ight an important difference between the obstructions, which limit the size of a stabilizable gap ball, in the time-varying and time-invaria nt cases. Several results on the gap metric and the gap topology are e stablished that are central in a geometric treatment of the robust sta bilizability problem in the gap. In particular, the concept of a ''gra phable'' subspace is introduced in the paper. Subspaces that fail to b e graphable are characterized by an index condition on a certain semi- Fredholm operator.