Stability analysis of systems with bounded additive uncertainties based on invariant sets: Stability and feasibility of MPC

In this paper the stability of constrained nonlinear discrete time systems with bounded additive uncertainty is analyzed. Sufficient conditions to guarantee that an autonomous constrained system is stable and ultimately bounded are given. These results are applied to MPC and sufficient conditions for stability and feasibility are obtained. The paper uses invariance set theory to extend the work of Scokaert et al. (1997), where asymptotic stability of MPC with decaying perturbation is analyzed, to bounded, non decaying, additive uncertainties.