It is shown that a simple modification (introducing a dead zone in the adaptation law) of the known adaptive high-gain control strategy u(t) = -k(t)y(t), k(t) = ||y(t)||2 yields lambda-tracking in the presence of output corrupted noise for a large class of reference signals and a large class of multivariable nonlinear minimum-phase systems of relative degree one. These results are applied to a realistic chemical reactor, showing the practical usefulness of these control laws.