Approximate Observer Error Linearization for Nonlinear Systems

This paper aims to explain a design method of state observers for nonlinear systems by approximate linearization of the error dynamics. For that, we give first the system description and problem formulation and then clarify the design method. In this method, we settle a state transformation matrix which transforms the nonlinear system approximately into an observable canonical form. Then, a state observer and its error are stated. After that, an approximation is made and a nonlinear observer gain is clarified. That linearizes the observer error dynamics.