  We propose a tube-based guaranteed cost model predictive controller
considering a homothetic formulation for constrained linear systems subject to
multiplicative structured norm-bounded uncertainties. It provides an upper
bound to the general min-max model predictive control. The invariance property
of the proposed tube holds for any arbitrary scaling. It yields a second-order
cone programming problem which is less computationally expensive than standard
semi-definite programming problems. We also present a numerical example with a
comparative study among the proposed approach, an open-loop guaranteed cost
model predictive controller, and a homothetic tube model predictive controller
for linear difference inclusion systems.
