Lyapunov-Schmidt method dedicated to the observer analysis and design

An analysis of observation error dynamics and an observer design are presented using the so-called Lyapunov-Schmidt method, firstly in order to analyze the solution's bifurcation of the observation error dynamics, and secondly in order to propose a robust observer with respect to such solution's bifurcation. Two numerical examples based on the Galerkin method show the pertinence of the proposed approach.