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 n steps, where n 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 λ-contractive sets. In fact, the new control scheme successfully stabilizes systems, where classical λ-contractive control laws fail.