Newton, observers and nonlinear discrete-time control

Development of exact asymptotic observers for nonlinear discrete-time systems is addressed. It is argued that instead of trying to imitate the linear observer theory, the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations. In particular, it is shown that Newton´s algorithm, properly interpreted, yields an asymptotic observer for a large class of discrete-time systems. The utility of the observer for closed-loop, observer-based, feedback control is also established. Some non-local aspects of the results are also discussed