Robust Control under Gap Metric and Pointwise Gap Metric Uncertainties *

A robust control theory based on describing uncertainties by metrics on the space of all systems has been developed in the past several years. This paper reviews some of the recent developments in this theory. The metrics used in this paper are the gap metric and the pointwise gap metric. The focus will be on the robust stability problem and certain robust performance problems for a feedback system with simultaneous plant and controller uncertainties. Fairly complete solutions are obtained for these problems. In this paper, the results obtained for the gap metric and the pointwise gap metric are parallelly presented, and show that the two metrics, although different, have a remarkable resemblance in properties.