Nonlinear time-varying controllers for robust stabilization

In this paper we consider the problem of robust stabilizallon 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 time-varying (NLTV) ones. Ihis, 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.