Robust feasibility in model predictive control: necessary and sufficient conditions

A number of results are derived for analysing the robust feasibility of a given model predictive control (MPC) scheme which ignores model mismatch and/or disturbances during control input computation. The main contribution of this paper is the development of computationally tractable tests for determining the robust feasibility of an MPC controller for linear or piecewise affine systems, where the constraints are given by the union of convex polyhedra and the disturbance acts additively on the state. Practical tests are also presented which allow one to give robust feasibility guarantees for all optimal and suboptimal MPC control actions.