  Some time ago we have derived from the QCD Lagrangian an equation of state
(EOS) for the cold quark matter, which can be considered an improved version of
the MIT bag model EOS. Compared to the latter, our equation of state reaches
higher values of the pressure at comparable baryon densities. This feature is
due to perturbative corrections and also to non-perturbative effects. Later we
applied this EOS to the study of compact stars, discussing the absolute
stability of quark matter and computing the mass-radius relation for self-bound
(strange) stars. We found maximum masses of the sequences with more than two
solar masses, in agreement with the recent experimental observations. In the
present work we include the magnetic field in the equation of state and study
how it changes the stability conditions and the mass-radius curves.
