On the maximal controller gain in linear MPC

The paper addresses the computation of Lipschitz constants for model predictive control (MPC) laws. Such Lipschitz constants are useful to assess the inherent robustness of nominal MPC for disturbed systems. It is shown that a Lipschitz constant can be computed by identifying the maximal controller gain of the MPC. Clearly, given the explicit description of the MPC, this gain can be easily identified. The computation of the explicit MPC may, however, be numerically demanding. The goal of the paper thus is to overestimate the maximal controller gain without using the explicit control law.