Robust stabilization of non-linear systems with unmodelled dynamics

Abstract

The problem of robust feedback stabilization of non-linear systems subject to two sources of uncertainties is considered. One source of uncertainty is introduced due to the presence of deterministic uncertain elements and parameters, and the other is due to the presence of unmodelled high frequency dynamics. The designed nonlinear controller is robust in the sense that every system trajectory is ultimately bounded within a neighbourhood of the equilibrium state. The controller is a continuous function of the states of the system and is composed of a ‘slow’, a ‘fast’, a ‘robust slow’, and a ‘robust fast’ control. This controller is the generalization of the well-known composite control strategy which has appeared in the singular perturbation literature.