A stabilizing control scheme for linear systems on controlled invariant sets

We present a new stabilizing control scheme for linear discrete-time systems with input and state constraints. Essentially, we seek a controller that is able to steer all initial states within a controlled invariant set towards the origin without violating the constraints. The control law builds on a predictive control scheme. We show that a prediction horizon of nn steps, where nn denotes the dimension of the system, is sufficient to solve the described control task. The proposed controller is related to but different from established feedback laws associated with λλ-contractive sets. In fact, the new control scheme successfully stabilizes systems, where classical λλ-contractive control laws fail.