This paper investigates the problem of robust
model predictive control (RMPC) of linear-time-invariant (LTI)
discrete-time systems subject to structured uncertainty and
bounded disturbances. Typically, the constrained RMPC
problem with state-feedback parameterizations is nonlinear
(and nonconvex) with a prohibitively high computational
burden for online implementation. To remedy this, a novel
approach is proposed to linearize the state-feedback RMPC
problem, with minimal conservatism, through the use of
semidefinite relaxation techniques. The proposed algorithm
computes the state-feedback gain and perturbation online
by solving a linear matrix inequality (LMI) optimization that,
in comparison to other schemes in the literature is shown
to have a substantially reduced computational burden
without adversely affecting the tracking performance of the
controller. Additionally, an offline strategy that provides
initial feasibility on the RMPC problem is presented. The
effectiveness of the proposed scheme is demonstrated
through numerical examples from the literature.