  In this work, we propose a tube-based model predictive control (MPC) scheme
for state and input constrained linear systems subject to dynamic uncertainties
described by integral quadratic constraints (IQCs). In particular, we extend
the framework of \r{ho}-hard IQCs for exponential stability analysis to
consider external inputs. This allows us to show that the model 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 MPC
scheme achieves robust constraint satisfaction and input-to-state stability in
the presence of dynamic uncertainties and additive bounded disturbances. In a
numerical example, we demonstrate the flexibility of the proposed tube dynamics
and the reduced conservatism of the IQC approach compared to other
characterizations of dynamic uncertainties that are used in robust MPC.
