Observer Design in Convergent Series for a Class of Nonlinear Systems

This paper deals with convergence analysis for power series solutions to a partial differential equation for nonlinear observer design with linear observer error dynamics. This power series solution is used to design the gain matrix for a Luenberger-like observer for nonlinear systems. An explicit domain of convergence around the origin is identified, which is related to the relative sizes of high-order terms in the original nonlinear system with respect to the linearized model. The convergent conditions can provide a guideline for nonlinear observer design with a truncated series for the observer gain.