On Simple Design of Nonlinear Observers for Robust Stabilization of Nonlinear Systems

Robust internal stabilization is a strong notion of stabilization, whereby stability is maintained regardless of small disturbances, noises, and uncertainties. In this paper, simple tools are developed for achieving robust internal stabilization of a rather large family of nonlinear systems. The main notion is that of a strict observer function, a function characterized by the following feature: subtracting a strict observer function from the differential equation of the controlled system results in an asymptotically stable differential equation. Strict observer functions are relatively easy to derive, and they directly yield robust asymptotic observers; the latter can be combined with robust state feedback controllers to achieve robust internal stabilization.