Input-to-state stability properties of relaxed barrier function based MPC**This work was supported by the Deutsche Forschungsgemeinschaft (Emmy-Noether-Grant, Novel Ways in Control and Computation, EB 425/2-1, and Cluster of Excellence in Simulation Technology, EXC 310/2)

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.