Nonlinear observer design for discrete-time bifurcating systems

This paper is a geometric study of the nonlinear observer design for discrete-time bifurcating systems. First, we obtain necessary and sufficient conditions for local exponential observers for discrete-time 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 discrete-time bifurcating systems. As applications of our observer design, we consider codimension one bifurcations such as the pitchfork bifurcation, and codimension two bifurcations such as the cusp bifurcation.