  This work proposes a novel robust model predictive control (MPC) algorithm
for linear systems affected by dynamic model uncertainty and exogenous
disturbances. The uncertainty is modeled using a linear fractional perturbation
structure with a time-varying perturbation matrix, enabling the algorithm to be
applied to a large model class. The MPC controller constructs a state tube as a
sequence of parameterized ellipsoidal sets to bound the state trajectories of
the system. The proposed approach results in a semidefinite program to be
solved online, whose size scales linearly with the order of the system. The
design of the state tube is formulated as an offline optimization problem,
which offers flexibility to impose desirable features such as robust invariance
on the terminal set. This contrasts with most existing tube MPC strategies
using polytopic sets in the state tube, which are difficult to design and whose
complexity grows combinatorially with the system order. The algorithm
guarantees constraint satisfaction, recursive feasibility, and stability of the
closed loop. The advantages of the algorithm are demonstrated using two
simulation studies.
