Robust stabilization of nonlinear systems, the separation theorem, and asymptotic observers

The problem of robustly stabilizing a nonlinear system is revisited through a re-examination of the separation theorem, whereby a nonlinear system can be stabilized by a combination of an asymptotic observer and a state feedback controller. The main emphasis is on the notion of strict asymptotic observers - asymptotic observers designed to tolerate uncertainty. It is shown that strict asymptotic observers can be constructed directly from strict observer functions - functions that yield an asymptotically stable differential equation when subtracted from the differential equation of the observed system.