Multiple model adaptive control. Part 1: Finite controller coverings

We consider the problem of determining an appropriate model set on which to design a set of controllers for a multiple model switching adaptive control scheme. We show that, given mild assumptions on the uncertainty set of linear time-invariant plant models, it is possible to determine a finite set of controllers such that for each plant in the uncertainty set, satisfactory performance will be obtained for some controller in the finite set. We also demonstrate how such a controller set may be found. The analysis exploits the Vinnicombe metric and the fact that the set of approximately band- and time-limited transfer functions is approximately finite-dimensional.