Stability conditions for observer based output feedback stabilization with nonlinear model predictive control

We consider the output feedback problem for continuous time systems using state feedback nonlinear model predictive control in combination with suitable state observers. Specifically we derive, for a broad class of state feedback nonlinear model predictive controllers, conditions on the observer that guarantee that the closed loop is semi-global practically stable. The derived results are based on the fact that predictive controllers that possess a continuous value function are to some extent inherently robust. To achieve semi-global practical stability one must basically require that the observer used achieves a sufficiently fast convergence of the estimation error. Since this in general a very stringent condition, we show that a series of observers such as high-gain observers, moving horizon observers and observers with finite convergence do satisfy it.