Robust output feedback control of nonlinear singularly perturbed systems

Abstract

In this work, we consider nonlinear singularly perturbed systems with time-varying uncertain variables, for which the fast subsystem is asymptotically stable and the slow subsystem is input/output linearizable and possesses input-to-state stable (ISS) inverse dynamics. For these systems, we synthesize a robust output feedback controller that ensures boundedness of the state and enforces robust asymptotic output tracking with attenuation of the effect of the uncertain variables on the output of the closed-loop system. The controller is constructed through combination of a high-gain observer with a robust state feedback controller synthesized via Lyapunov's direct method. The proposed controller enforces the aforementioned properties in the closed-loop system, for initial conditions, uncertainty and rate of change of uncertainty in arbitrarily large compact sets, provided that the singular perturbation parameter is sufficiently small and the observer gain is sufficiently large.