On slowly varying systems - l-infinity to l-infinity performance and implications to robust adaptive control

The authors present a result on the l-infinity to l-infinity performance of slowly time varying systems. In particular, it is shown that the performance of such systems cannot be much worse than that of the frozen-time systems which are time invariant. This result is used to characterize a class of indirect adaptive controllers that can stabilize a time-invariant system subjected to both parametric and l-infinity to l-infinity bounded unstructured uncertainty. Pertaining to this class of controllers, a particular indirect adaptive scheme is proposed that provides the greatest upper bound on the size of the unstructured uncertainty for which stability is ensured.