On the stability of MPC with a finite input alphabet

This paper studies stability of Model Predictive Control for systems with a finite input alphabet. Since this kind of systems may present a steady-state error under closed-loop control, the forms is on stability in the sense of ultimate boundedness of solutions. To derive sufficient conditions for stability, two different approaches are presented. The first one approximates the finite input alphabet via saturation-control allowing us to analyze the problem from a robust control perspective. In the second approach, a direct analysis of the problem is carried out. The results thus obtained are shown to be less conservative regarding ultimate bounded set than those obtained via the robust control approach.