On the stability of nonlinear plants that include an observer for their feedback linearization

The states of a plant are required to achieve exact linearization via state feedback and transformation. This calls for an observer when all the plant states are not directly accessible, then the linearizing feedback law can be implemented with the observer estimates. We analyse this situation from a stability point of view, for a class of nonlinear systems and a class of observers. Morever, we set a sufficient condition that makes possible the stabilization of the whole feedback system: the plant, the observer and the (linearizing) feedback law. From this condition, which depends on the observer gains and the linear feedback gains, we find a region for these parameters where the stability of the whole system is guaranteed.