  In this work, we propose a tube-based MPC scheme for state- and
input-constrained linear systems subject to dynamic uncertainties characterized
by dynamic integral quadratic constraints (IQCs). In particular, we extend the
framework of $\rho$-hard IQCs for exponential stability analysis to external
inputs. This result yields that the error between the true uncertain system and
the nominal prediction model is bounded by an exponentially stable scalar
system. In the proposed tube-based MPC scheme, the state of this error bounding
system is predicted along with the nominal model and used as a scaling
parameter for the tube size. We prove that this method achieves robust
constraint satisfaction and input-to-state stability despite dynamic
uncertainties and additive bounded disturbances. A numerical example
demonstrates the reduced conservatism of this IQC approach compared to
state-of-the-art robust MPC approaches for dynamic uncertainties.
