On the modified Minkowski functional minimization controller for uncertain systems with input and state constraints

Two new stabilizing control schemes are presented for uncertain linear constrained systems on a controlled invariant set C. The first scheme is an extension of the control law in Blanchini (1994), where the requirement that C is contractive in one step is relaxed. The second scheme aims to improve the performance by using a modified Minkowski functional concept. Proofs of recursive feasibility and robust asymptotic stability are provided. One numerical example with comparison to earlier solutions shows the main benefits of the proposed methods.