Stabilization of inexact MPC schemes

In model predictive control often the underlying optimization problem is not solved exactly to meet hard real-time bounds or to save computations. This jeopardizes properties of the closed loop system, such as stability, performance or recursive feasibility. We present a framework for linear system with polytopic constraints and quadratic performance criteria, which guarantees recursive feasibility and stability subject to inexact solutions. We combine the approach with simple optimization methods to obtain real-time feasibility and stability.