Abstract
Using the center manifold theory for maps in a systematic way, the authors present in this note a necessary condition and sufficient conditions for discrete-time nonlinear systems to be stabilizable via smooth state feedback. Then, the authors derive a necessary and sufficient condition characterizing the existence of exponential observers for Lyapunov stable discrete-time nonlinear systems. This, in turn, leads to a separation principle for the asymptotic stabilization problem. As an application, the output regulation problem is solved via error feedback.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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