THE RELATIONSHIP BETWEEN GAP METRIC AND TIME-VARYING GAP METRIC FOR LINEAR TIME-VARYING SYSTEMS

摘要

This paper is concerned with the relationship between the gap metric and the time-varying gap metric for linear time-varying systems in the feedback configuration. It is shown that these two kinds of gaps are identical to each other when we measure the distance between corresponding graphs of a plant and a controller in a feedback system. This result supplies a simple way for computing the supremum appearing in the definition of the time-varying gap. Furthermore, the developed criteria are also applied to compute the optimal minimal angles of stabilizable linear time-varying systems.