The problem of stabilization of linear discrete-time periodic systems is co
nsidered. LMI based conditions for stabilization via static periodic state
feedback as well as via static periodic output feedback are presented. In t
he case of state feedback, the conditions are necessary and sufficient wher
eas for output feedback the result is only sufficient as it depends on the
particular state-space representation used to describe the system. The prob
lem of quadratic stabilization in the presence of either norm-bounded or po
lytopic parameter uncertainty is also treated. As an application of the out
put feedback stabilization technique, we consider the problem of designing
a stabilizing (respectively, quadratically stabilizing) static periodic out
put feedback controller for linear time-invariant discrete-time systems whi
ch are not stabilizable (respectively, quadratically stabilizable) by stati
c constant output feedback.