UNSTABLE SYSTEMS AND FEEDBACK: THE GAP METRIC.

This paper is concerned with unstable input-output systems which are stabilized by feedback in the presence of uncertainty. A metric on unstable systems in terms of the gap between their graphs in a Hilbert space is introduced. It is shown that the tolerable open-loop uncertainties are precisely those that are small in gap, and that every ″continuously robust″ metric on unstable systems is equivalent to the gap metric.