Submitted to the 38th IEEE Conference on Decision and Control, 1999.
Gap Metric Performance Bounds for Linear Feedback
Systems
Michael Cantoni
Abstract
Upper and lower bounds on the difference in the performance of two
linear, possibly infinite-dimensional and time-varying, stable
feedback-systems that involve the same controller are derived in terms
of the gap between the plants. To this end, the underlying geometry of
the robust feedback stabilisation problem is exploited. The advantage
of such an approach is that no specific system representation is
required. With regard to extending the results to non-linear systems,
a simple example is presented to show that the upper bound does not
hold in general when the controller (in common) is non-linear.
Keywords : Linear Feedback Systems, Robust Performance,
Gap Metric, Parallel Projections.