Robust exponential stability of full state and observer feedback controlled systems is explored in the context of predictive control. The total stability theorem is used to ensure exponential stability via bounds on model, modelling error and control gain characteristics in two scenarios of differing complexities. Sufficient conditions are obtained to ensure an observed, nonlinear plant's state trajectory stays within a fixed distance of an exponentially stable, controlled, model state trajectory. These results have applications in predictive control, where model-based receding-horizon designs are used to yield robust solutions on the infinite-horizon.