Convergent Series Observer Design 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. The conditions are identified to guarantee the convergence of the series in l(2). The linearized model of the original system is assumed to be anti-stable at the origin for the convenience of presentation. The convergent conditions can provide a guideline for nonlinear observer design with a truncated series for the observer gain.