On slowly varying systems: L∞ to L∞ performance and implications to robust adaptive control

In this paper we present a result on the L^∞ to L^∞ performance of slowly time varying systems. In particular we show 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^∞ to L^∞ 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.