Nonlinear Discrete-Time Observers using Newton´s and Broyden´s Method

In this note we study observers for a general class of nonlinear discrete-time systems, using Newton´s method in the context of solving a sequence of nonlinear equations. The proposed observer is shown to have non-local convergence properties, however, it is potentially computationally expensive. We discuss the possibility of reducing the computational complexity of this observer by implementing it with a modified version of Broyden´s method.