Nonlinear observer design for bifurcating systems

This paper is a geometric study of the nonlinear observer design for bifurcating systems. First, we obtain necessary and sufficient conditions for local exponential observers for nonlinear bifurcating systems under some stability assumptions. Next, using our characterization of local exponential observers, we derive a construction procedure for exponential observers for the bifurcating systems. As applications of our observer design, we consider codimension one bifurcations such as the pitchfork and Hopf bifurcations, and codimension two bifurcations such as the cusp bifurcation.