Robust stabilization via nonlinear time-varying feedback

In this paper we consider the problem of robust stabilization for a certain class of plants with unstructured, infinite dimensional uncertainty. We demonstrate that for the problem of robustly stabilizing this class of plants, linear time--invariant controllers perform as well as nonlinear lime-varying (NLTV) ones. This, in particular, implies that adaptive control laws offer no advantage as far as the problem of robust stabilization of this class of plants is concerned. As a corollary we demonstrate that the small-gain theorem is both necessary and sufficient for a certain class of NLTV operators.