  Motivated by the possibility of radiation driven instabilities in rotating
magnetic stars, we study the stability properties of general linear
perturbations of a stationary and axisymmetric, infinitely conducting perfect
fluid configuration threaded by a magnetic field and surrounded by vacuum. We
develop a Lagrangian perturbation framework which enables us to formulate a
strict stability criterion based on the notion of a canonical energy (a
functional of the fluid displacement $\xi $ and its first time derivative). For
any given choice of $\{\xi,\partial_t \xi \} $, the sign of the canonical
energy determines whether the configuration is stable or not at the linear
level. Our analysis provides the first complete description of the stability
problem for a magnetic star, allowing for both rotation and the presence of a
magnetic field in the exterior vacuum region. A key feature of the Lagrangian
formulation is the existence of so-called `trivial' fluid displacements, which
do not represent true physical perturbations. In order for the stability
criterion to make rigorous sense one has to isolate these trivials and consider
only the physical `canonical' displacements. We discuss this problem and
formulate a condition which must be satisfied by all canonical displacements.
Having obtained a well-defined stability criterion we provide examples which
indicate that the magnetic field has a stabilising effect on radiation driven
instabilities.
