On the use of algebraic geometry for the design of high-gain observers for continuous-time polynomial systems

The goal of this paper is to apply some concepts and techniques from algebraic geometry to study the observability of nonlinear continuous-time polynomial systems. After deriving some new results for observability and embeddings, it is shown how to use such concepts to easily design high-gain observers. The proposed technique is illustrated by an application to the well known Rossler oscillator.