Robust stabilization and performance recovery of nonlinear systems with input unmodeled dynamics

In this paper we extend the time-scale separation redesign for stabilization and performance recovery of uncertain nonlinear systems proposed in and to systems with input unmodeled dynamics. The class of unmodeled dynamics studied are relative degree zero and minimum phase. We design two sets of high gain filters - the first to estimate the uncertain input to the plant over a fast time-scale, and the second to force this estimate to converge to the nominal input on an intermediate time-scale. The control input then acts over the slow time-scale and guarantees that the closed-loop trajectories approach those of the nominal system.