Input-to-state stability properties of relaxed barrier function based MPC*

We analyze robust stability properties of linear model predictive control schemes that are based on relaxed logarithmic barrier functions. It is shown that the corresponding closedloop system is globally exponentially stable in the nominal case as well as input-to-state stable with respect to arbitrary additive disturbances. Possible benefits and the practical relevance of the presented approach are discussed and illustrated by means of a numerical example.