On discrete-time nonlinear control

The authors first derive a necessary condition and some sufficient conditions for a class of discrete-time nonlinear systems to be asymptotically stabilizable via smooth state feedback. Then, the authors investigate a necessary and sufficient condition characterizing the existence of exponential observers for Lyapunov stable discrete-time autonomous systems. This condition, together with the previous stabilization results, leads to a separation principle for asymptotic stabilization in discrete-time. As an application, the authors solve the error feedback regulator problem