A Three-time-scale redesign for robust stabilization and performance recovery of nonlinear systems with input uncertainties

In this paper we propose a robust redesign technique which recovers the trajectories of a nominal control design in the presence of input uncertainties. We design two sets of high gain filters - the first to estimate the input uncertainty over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time- scale. Using singular perturbation theory we prove that the trajectories of the resulting three-time scale redesigned system approach those of the nominal system when the filter gains are increased.