A Two-Time-Scale Redesign for Robust Stabilization and Performance Recovery of Uncertain Nonlinear Systems

In this paper we propose a robust redesign technique which recovers the trajectories of a nominal control design in the presence of additive input uncertainties. We design a high-gain filter and employ the fast variables arising from this filter in the feedback control law to cancel the effect of the uncertainties in the plant. Using singular perturbation theory we prove that the trajectories of the redesigned system approach those of the nominal system when the filter gain is increased. We illustrate the redesign by applying it to two physically motivated examples.